If Black holes slowly evaporate over time is there a point where they stop being a black hole?

[Carrock]

1 hour ago, swansont said:

You don’t quote (including enough for proper context) or link to this claim. That’s what I mean by not bringing the receipts. 

 

I tried a proper quote, and crashed the editor, luckily only losing a minute's work.

May 3rd

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.... the matter particle escapes to infinity while the antimatter particle falls in. Its a rather simplistic descriptive but the mass loss is due to being the anti particle of the pair. A photon is its own antiparticle. The difference between them isn't charge but rather its polarity. As a wave it obeys constructive and destructive interference. So anti-photons will annihilate with matter photons. ......

 

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The mention that I saw was here, in the context of Hawking radiation, and the particle that reduces the mass of the BH is indeed associated with a negative energy, because it’s a virtual particle/antiparticle pair. That’s why the mass decreases, and how you get real particles emitted as radiation.

A definite lack of receipts....

Without references I find that fully as plausible as Mordred's matter photons, which I suspect is the intention.

If e.g. a positron is emitted, the particle absorbed can't be (I think) a virtual electron because of violation of charge conservation and the possibility due to local anomalies that it will never be a real particle.

 

A particle/antiparticle pair (not virtual):

The absorbed particle is calculated as having negative energy by a distant observer due to its being far down the BH's gravity well and falling into the BH. The emitted particle necessarily has positive energy since it will escape the black hole.

 

Loosely speaking

Viewed from the centre of mass of the particle/antiparticle pair (over a very short distance where the gravitational tide is relatively constant) both particles will gain kinetic energy or blue shift as tidal forces pull them apart. The centre of mass is falling at high speed into the black hole and ( required by energy conservation ) the infalling particle's negative gravitational energy (wrt infinity) is greater than its mass-energy.

 

I could be completely wrong... interesting to see where this goes.

[Mordred]

Lets get a couple of details out in the open. I'd like to quote a certain section of the link I lasted posted.

to quote.

In conclusion, we started with a negative energy solution of the Dirac equation and we end up with a solution which has positive energy and reversed 3-momentum. Indeed, if we reverse the momentum 4-vector this is identical with one of the positive energy solutions of Lecture 6. Hence, by reversing the momentum 4-vector of the negative energy solutions we obtain solutions which describe antiparticles with positive energy (physical particles).

  Another observation is that we started with a negative energy particle solution, which moves backward in time, since p 0 = E < 0 , and we found that this is equivalent to an antiparticle solution which has positive energy and moves forward in time because p 0 = ∣E∣ > 0 . In other words, negative energy particle solutions going backwards in time describe antiparticle solutions which have positive energy and move forward in time.

Now think in terms of those particle antiparticles with regards to Hawking radiation.

key note the statement " The physical antiparticle is a positive energy solution" 

you can certainly model as a negative solution but the physical antiparticle will always have positive energy.

Hence you need to understand the charge conjugation terms and how that term includes the particle momentum and helicity terms. In QFT for Lorentz invariance the Klein Gordon is used as opposed the Schrodinger. Unfortunately that is the method I most commonly use for anything relating to particle physics. So that is the method I typically use when answering questions relating to anything involving particles. This includes Hawking radiation.  As noted the antiparticle has positive energy. Even though literature often refer to the negative energy solutions.

Hawking radiation articles also don't typically cover the charge conjugation aspects that identify and define the particle/ antiparticle. In higher grade articles such as arxiv articles your already already to expected to know this detail.

 

Edited July 30 by Mordred

[Carrock]

12 hours ago, Mordred said:

I'm getting tired of accusations from posters that never show any mathematical argument to support their claims. I think I am well within my right that if someone claims I am wrong they are expected to prove just that beyond bland statements.

For example those equations you posted Carrock are contained in  textbooks on Cosmology with regards to the thermodynamics. Accusing me of pseudoscience when I am describing textbook equations and relations doesn't work in your favor

Clearly you speed read this post.

Quote

 

PS I'm sorry you have a problem with thermodynamic applications in Cosmology. However that is the way it is.

 

Edit: seeing as you did find the errors I'll grant a +1

 

You'll never let me live down admitting being wrong about pv=nRt will you?

I think my claim you are incompetent at calculus is amply proved. (More than) three out of fourteen of your equations were flawed and I don't recall you spotting errors I didn't point out.

I never accused you of pseudoscience when you were describing referenced textbook equations as you couldn't claim them as evidence of mass photons and antiphotons.

It's moot now as you have been put to the question and renounced pseudoscience.

 

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For one thing I have never seen this article before I don't use screen shot reference papers from some lecture for something inclusive in standard textbooks.

The reason those equations look familiar is precisely for the detail they are in standard textbooks.

Many of your equations don't look familiar.

Which textbooks? Many of those eqns aren't in 'screen shot reference papers from some lecture' but appear to have been modified by you, introducing errors that don't look like typos.

No one seems to have picked up on my belief that those cosmology lectures with more text linking more equations may be easier to learn from than a post that hasn't been been reviewed by critical students.

[Mordred]

I didn't speed read the article that article describes how particle physics in mainstream physics describes an anti particle. 

 The thing is not once have you ever posted anything mathematicsvof your own to ever show I have been incorrect on something in every single claim of my being incorrect in any post where you and I have a conflict in understanding.

I have done in nearly every instance. You have not. Nor have you ever bothered posting any reference showing where I am in error beyond blind assertions that I am.

You wanted a reference you got one. In regards to thermodynamics you already know from the link you already provided yourself that the FLRW metric models expansion as an adiabatic and isentropic expansion.

That is the basis behind the equations of state the FLRW metric uses for the acceleration equation.

Your last post has always been your typical tactic. Ignore Any reference given.

That last reference is a CERN lecture note.

Your refusal to accept my answers even when references have been provided in those past conversations does not mean I am talking pseudoscience. That is a false accusation.

 

To put it bluntly not once have you ever provided any mathematics or reference paper showing any claim of me being incorrect. (Not once)

 That is precisely why I don't waste my time defending myself vs your accusations. You never do the same steps you require from me ie supplying references as one example.

As far as those equations I provided in regards to thermodynamics the textbook those equations came was from my notes from when I was studying Andrew Liddles textbook. Years back I might add . That was back when I was trying to find more classical treatments for the benefit of the average poster on this forum.

Edited July 30 by Mordred

[swansont]

7 hours ago, Carrock said:

Without references I find that fully as plausible as Mordred's matter photons, which I suspect is the intention.

I took that as differentiating between the particle and the antiparticle. matter vs antimatter.

[Mordred]

41 minutes ago, swansont said:

I took that as differentiating between the particle and the antiparticle. matter vs antimatter.

So do I the problem with Harking radiation is that he never did specify which particle/antiparticle pair is used. There is a reference I believe already posted in this thread though will have to double check that after work mentioning that detail. That same paper examines different gauge bosons in regards to Hawking radiation and the ramifications of each using the ( cpt) symmetry relations.

The reason photons are typically used is it is the mediator for blackbody temperatures. 

Edited July 30 by Mordred

[Carrock]

28 minutes ago, swansont said:

I took that as differentiating between the particle and the antiparticle. matter vs antimatter.

Swansont said:

Quote

The mention that I saw was here, in the context of Hawking radiation, and the particle that reduces the mass of the BH is indeed associated with a negative energy, because it’s a virtual particle/antiparticle pair. That’s why the mass decreases, and how you get real particles emitted as radiation.

Do you maintain this view, which seems contrary to my view of particles with locally positive energy? It's unnecessary, and inconsistent with my understanding of physics.

 

 

[swansont]

2 hours ago, Carrock said:

Do you maintain this view, which seems contrary to my view of particles with locally positive energy? It's unnecessary, and inconsistent with my understanding of physics.

You learned that virtual particles have positive energy? What happens when the pair annihilates?

[Carrock]

3 hours ago, Mordred said:

I didn't speed read the article that article describes how particle physics in mainstream physics describes an anti particle. 

 The thing is not once have you ever posted anything mathematicsvof your own to ever show I have been incorrect on something in every single claim of my being incorrect in any post where you and I have a conflict in understanding.

I have done in nearly every instance. You have not. Nor have you ever bothered posting any reference showing where I am in error beyond blind assertions that I am.

You wanted a reference you got one. In regards to thermodynamics you already know from the link you already provided yourself that the FLRW metric models expansion as an adiabatic and isentropic expansion.

That is the basis behind the equations of state the FLRW metric uses for the acceleration equation.

Your last post has always been your typical tactic. Ignore Any reference given.

That last reference is a CERN lecture note.

Your refusal to accept my answers even when references have been provided in those past conversations does not mean I am talking pseudoscience. That is a false accusation.

 

To put it bluntly not once have you ever provided any mathematics or reference paper showing any claim of me being incorrect. (Not once)

 That is precisely why I don't waste my time defending myself vs your accusations. You never do the same steps you require from me ie supplying references as one example.

As far as those equations I provided in regards to thermodynamics the textbook those equations came was from my notes from when I was studying Andrew Liddles textbook. Years back I might add . That was back when I was trying to find more classical treatments for the benefit of the average poster on this forum.

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I didn't speed read the article that article describes how particle physics in mainstream physics describes an anti particle. 

Relax. No one here cares.

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 The thing is not once have you ever posted anything mathematicsvof your own to ever show I have been incorrect on something in every single claim of my being incorrect in any post where you and I have a conflict in understanding.

I have done in nearly every instance. You have not. Nor have you ever bothered posting any reference showing where I am in error beyond blind assertions that I am.

All your cosmology eqns: (more than) three in fourteen had errors. I didn't provide maths of my own; just ordinary, correct maths.

You naturally complained when I left you to fix some of your own errors.

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Nor have you ever bothered posting any reference

You ignored references I provided i.e.  cosmology lectures  and dimensional analysis.

I even provided a worked dimensional analysis example in a second post. You complained I hadn't done enough to fix your equations and to this day you haven't mastered dimensional analysis (even the equation checking version), something which took me a fraction of a maths lesson when I was 14.

 

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You wanted a reference you got one.

It's very thoughtful, but you shouldn't just assume people want things. You've already given me a hundred references we'll both enjoy reading for the first time in our old age. Time to honour someone else.

 

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In regards to thermodynamics you already know from the link you already provided yourself that the FLRW metric models expansion as an adiabatic and isentropic expansion.

That is the basis behind the equations of state the FLRW metric uses for the acceleration equation.

What are you on?

 

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Your last post has always been your typical tactic. Ignore Any reference given.

That last reference is a CERN lecture note.

Your refusal to accept my answers even when references have been provided in those past conversations does not mean I am talking pseudoscience. That is a false accusation.

 

To put it bluntly not once have you ever provided any mathematics or reference paper showing any claim of me being incorrect. (Not once)

 That is precisely why I don't waste my time defending myself vs your accusations. You never do the same steps you require from me ie supplying references as one example.

An extreme case of projection. I've only sent you two references in recent years and you ignored

both of them.

"To put it bluntly not once have you ever provided any mathematics or reference paper showing any claim of [Mordred] being incorrect"

It's rather sad but people rarely write papers claiming people with outlandish ideas are wrong.

Whether it's claiming you can fly the Atlantic by flapping your arms really hard, or the earth will soon be under attack by deadly matter photons, you'll probably find some bean counter has refused to fund any research.

 

 

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Your refusal to accept my answers even when references have been provided in those past conversations does not mean I am talking pseudoscience. That is a false accusation.

Non sequitur

You've been put to the question and given up any aspiration to be a pseudoscientist. Give it a rest.

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As far as those equations I provided in regards to thermodynamics the textbook those equations came was from my notes from when I was studying Andrew Liddles textbook. Years back I might add . That was back when I was trying to find more classical treatments for the benefit of the average poster on this forum.

Maybe you should buy the book. It would be interesting to know what edition you used, and what went so horribly wrong.

Edited July 30 by Carrock
missed part of post

[Mordred]

Correct not once have you ever math yourself glad we agree on that. You have never done in any of your claims of me applying pseudoscience. Nor have you ever supplied any reference showing an error in my thinking.

Here is a little detail those statistical mechanics  terms are simply reminder relations of what gets involved when one describes an adiabatic and isentropic system they aren't even used by the FLRW metric itself.

 The equations of state relations are what gets used.

Those statistical mechanical terms are simply heuristic reminders. They aren't essential to the FLRW metric the equations of state are.

 

Edited July 30 by Mordred

[Carrock]

24 minutes ago, swansont said:

You learned that virtual particles have positive energy? What happens when the pair annihilates?

In a reference frame where they have positive energy their energy can drop/rise until they're indistinguishable from the background. Unless they become a particle/antiparticle pair their existence is extremely brief.   (10^-34 JS?)

Virtual particles are not particles as such. You seem to require a virtual particle to fall into the BH while a real particle escapes and don't worry about conservation of charge if it's e.g. an electron.

Choose a suitable reference and anywhere outside a BH can have positive or negative (gravitational) energy.

I really don't see the point of choosing a coordinate system with negative energy particles purely so that an asymmetry can make odd things seem possible. From a suitable reference, as I said, the particles spread out fairly symmetrically at first, with no great difference between the particles.

 

The only reason to have all these mass photons, virtual positrons etc is to have a weird fake theory which gives the same results as Hawking etc predicted. If Hawking etc are wrong, black holes will get heavier, if they're right, ordinary particle pairs form, most end up in the black hole but a lucky few individuals escape.

[swansont]

18 minutes ago, Carrock said:

In a reference frame where they have positive energy their energy can drop/rise until they're indistinguishable from the background. Unless they become a particle/antiparticle pair their existence is extremely brief.   (10^-34 JS?)

But if they have positive energy, when they annihilate you have energy where you had none before, which means energy is not conserved.

18 minutes ago, Carrock said:

Virtual particles are not particles as such. You seem to require a virtual particle to fall into the BH while a real particle escapes

It’s not what I require, it’s what the description of Hawking radiation requires.

18 minutes ago, Carrock said:

and don't worry about conservation of charge if it's e.g. an electron.

Not sure where this comes from

 

18 minutes ago, Carrock said:

Choose a suitable reference and anywhere outside a BH can have positive or negative (gravitational) energy.

We’re talking about the virtual pair, though, without other constraints. IIRC the magnitude of the gravitational PE is less than the mass energy in this situation, so one particle escaping has to result in a loss of energy from the BH.

18 minutes ago, Carrock said:

I really don't see the point of choosing a coordinate system with negative energy particles purely so that an asymmetry can make odd things seem possible. From a suitable reference, as I said, the particles spread out fairly symmetrically at first, with no great difference between the particles.

The coordinate system isn’t going to matter (it can’t; you can’t have something that happens in one frame be impossible in another)

18 minutes ago, Carrock said:

The only reason to have all these mass photons, virtual positrons etc is to have a weird fake theory which gives the same results as Hawking etc predicted. If Hawking etc are wrong, black holes will get heavier, if they're right, ordinary particle pairs form, most end up in the black hole but a lucky few individuals escape.

It’s not a weird, fake theory. This is a common description of Hawking radiation.

https://www.sciencealert.com/hawking-radiation#

http://www.physics.hmc.edu/student_projects/astro62/hawking_radiation/radiation.html

 

[Carrock]

21 minutes ago, Mordred said:

Correct not once have you ever math yourself glad we agree on that. You have never done in any of your claims of me applying pseudoscience. Nor have you ever supplied any reference showing an error in my thinking.

 I supplied cosmology lectures  showing multiple errors in your thinking. Of course you didn't read it..

 

Weird concept

1 hour ago, Carrock said:

I didn't provide maths of my own; just ordinary, correct maths.

So, Mordred, when you 'math' yourself you provide brilliant wrong maths you've invented yourself. No wonder you're careful not to provide sources which would make it harder to maintain your fantasies.

'Mathing' you would be like stealing a child's pocket money.

 

[swansont]

6 hours ago, Carrock said:

No one seems to have picked up on my belief that those cosmology lectures with more text linking more equations may be easier to learn from than a post that hasn't been been reviewed by critical students.

I think this is moot; this isn’t a lecture, it’s a discussion forum. I think it’s an unreasonable expectation.

I don’t see where you’ve typed in all that many equations in these discussions. I wonder, if you had done so, if your typing skill would stand up to the same scrutiny and criticism you have offered up.

[Mordred]

As I stated any errors in those statements do not particularly matter as those relations are not part of the calculations involved for the acceleration equation used by the FLRW metric itself 

Those are nothing more than heuristic reminders as an assist they have zero importance to the FLRW metric beyond a brief description of what an adiabatic and isentropic  system entails.

Those posts your referring to was also several years ago. The only relevant mistake was trying to find some heuristic way to get the thermodynamic relations involved through to you in the first place instead of using related Euler langrangian equations which actually determine the energy/density to pressure relations.

 Quite frankly your making me regret trying to use a heuristic explanation to get you to understand it at that time 

16 minutes ago, swansont said:

I think this is moot; this isn’t a lecture, it’s a discussion forum. I think it’s an unreasonable expectation.

I don’t see where you’ve typed in all that many equations in these discussions. I wonder, if you had done so, if your typing skill would stand up to the same scrutiny and criticism you have offered up.

Truthfully I would thoroughly enjoy watching Carrock struggle  for several hours on a single post full of equations in latex.

Some of my larger posts full of equations can take me up to 8 hours to get through. It's extremely easy to miss typos under those circumstances.

It has nothing to do with struggling with the math for all my edits. It's literally fixing latex errors and saving often so I don't lose those latex expressions already done.

Edited July 30 by Mordred

[Carrock]

1 hour ago, Mordred said:

Truthfully I would thoroughly enjoy watching Carrock struggle  for several hours on a single post full of equations in latex.

 

3 hours ago, swansont said:

3 hours ago, Carrock said:

Virtual particles are not particles as such. You seem to require a virtual particle to fall into the BH while a real particle escapes

It’s not what I require, it’s what the description of Hawking radiation requires.

I get the point

Bye

[Airbrush]

On 4/27/2024 at 11:46 AM, MSC said:

If black holes slowly loss mass over time; is there a point where they stop being black holes and devolve into something more like a neutron star? 

https://news.ubc.ca/2024/04/05/new-gravitational-wave-signal-neutron-stars-and-black-holes/#:~:text=The 'mass gap'%2C spanning,theory than an empty gap.

If so; would that explain the potential existence of objects falling within the mass gap between small black holes and neutrons stars? Objects that may have been detected in gravitational wave data? Incredibly old ex-black holes? Dying Holes. 

If there is a singularity at the center of a black hole, a point of near infinite density, would that same point also be a point of near infinite pressure? All that mass trying to explode outward while the gravitational force of itself keeps everything packed in.

Extra question; is the idea a theory or a hypothesis? Explain that one like I'm 5.

"As a black hole evaporates, it loses mass and eventually disappears in a final burst of energy, leaving behind no singularity, just dispersed radiation and particles."

 "Theoretical models suggest that when the black hole reaches a critical size, it might release a final, intense burst of radiation, possibly equivalent to the energy of several megatons of TNT. This burst would signify the complete evaporation of the black hole.  After this burst, the black hole would effectively disappear, leaving behind only the radiation and particles it emitted during its evaporation. There would be no remaining singularity or event horizon—just the energy and particles dispersed into space."

Edited August 14 by Airbrush

[MigL]

4 hours ago, Airbrush said:

There would be no remaining singularity or event horizon—just the energy and particles dispersed into space

Unfortunately that violates a quantum mechanical property called unitarity, and is at the heart of the BH information paradox.

[Airbrush]

16 hours ago, MigL said:

Unfortunately that violates a quantum mechanical property called unitarity, and is at the heart of the BH information paradox.

Ok there.  You got me with a concept new to me "unitarity" which sounds very cool!  So, I asked ChatGPT what it was and here is what I got:

"Unitarity is a fundamental concept in quantum mechanics that ensures the conservation of probability. It is related to the time evolution of quantum states,

Conservation of Probability: In quantum mechanics, the total probability of all possible outcomes of a measurement must always sum to one. Unitarity guarantees this by ensuring that the quantum state's evolution preserves the norm (or length) of the state vector.

Unitary Operators: The time evolution of a quantum system is described by a unitary operator U(t)U(t)

Unitarity ensures that quantum mechanics is a consistent and physically meaningful theory. It prevents probabilities from becoming negative or exceeding one, and it ensures that the evolution of quantum states is reversible."

I don't understand any of that.  Can you translate that into English?  Why would anything remain after a black hole explodes near the end of its' evaporation?  All that remains is photons, right?

[Mordred]

Unitary is equivalent to normalized in essence.

So take a unit vector that unit vector is normalized to value 1. So for example

\(c=\hbar=K=1\)  Now as you cannot have a negative probability by multiplying the square of the probability amplitude you get a positive value. The conserved portion requires a closed group or system where you have no forces involved for conservation of momentum example being the Schrodinger equation you normalize the group and that group is finite. Example 1 loop integral is a closed group. 

That's a rough and gritty explanation the details get more intense.

Edited August 15 by Mordred

[MigL]

Whoah!
That is 'rough and gritty'.
Unitarity simply means that the measured state of a system can be related to previous states by a unitary operator.
Thus QM implies that information cannot be lost through time evolution of states.
Not even beyond the Event Horizon of a BH.

[Mordred]

Key word Unitary operator. For example how is an operator defined under QM ? What makes that operator Unitary?

2 key operators in QM position and momentum. These however are not the Unitary operators

1 hour ago, MigL said:

Unitarity simply means that the measured state of a system can be related to previous states by a unitary operator.
 

Doesn't describe the Unitary operator itself given as

\[U^\ast U=1\]

 

The Unitary operator must preserve the inner product of the Hilbert space.

Keep in mind I'm trying to avoid terminology such as bounded, isomorphism , adjoint etc.

An easy example is the rotation matrices these are Unitary operators. A unitary operator can change to orientation, coordinates or state itself but cannot change the magnitude (norm of the state).

Every Unitary operator is normal.

Categories of Unitary operators being Unitary space, Unitary transformation, or Unitary matrix.

A Unitary space is a complex vector field with a distinguished positive definate Hermitean form

A Unitiary transform is a surjective transform between two Unitary spaces U,V.

A Unitary matrix is a complex valued matrix whose inverse is equal to its conjugate transpose.

See why I stated very rough and gritty in the above ?

 

 

Edited August 15 by Mordred

[Mordred]

Lets do a simple example (though unless you understand QM won't really be simple)

Unitary space

\[\langle u,v\rangle=\mathbb{C}^n\]

you have the inner products of a complex unitary space (Hilbert space).

In terms of the Schrodinger equation the continous evolution must take the form

\[\rho\rightarrow U\rho U^\dagger\] 

where U is the unitary operator.

the Hamilton governing this is 

\[H=\sum^d_{j=1}\lambda_j|j\rangle\langle j|\]

which gives unitary form

\[U=\sum^d_{j=1}e^{\lambda_j t}|j\rangle\langle j|\]

 

in other words one requires a bit of preliminary mathematics and QM to understand the above.

Example the d above the sum is not  dimension it is an integer defined by a renormalization scheme. Seeing that above the sum automatically tells me its a normalized state 

Edited August 15 by Mordred

[joigus]

25 minutes ago, Mordred said:

which gives unitary form

 

U=∑j=1deλjt|j〉〈j|

 

 

in other words one requires a bit of preliminary mathematics and QM to understand the above

You forgot a -i in the exponent, Mordred. You are under arrest for violating unitarity. 🤣

[Mordred]

not quite lol though still +1

\[e^{\lambda_j t}\]

is the directional derivative taking the previous Hamilton statement under spectral decomposition.

see here in regards to Hermitean directional derivatives

https://en.wikipedia.org/wiki/Matrix_exponential

look under Directional derivatives under

\[G_{ij}\]

though I  will use my get out of jail card for forgetting to mention its a restricted directional example for simplification.

Your likely more familiar with the form 

\[H|\psi(t)\rangle=i\hbar|\psi(t)\]

\[\psi(t)=exp(-\frac{iH(t)}{\hbar})\]

\[U=exp(-\frac{iH(t)}{\hbar})\]

 

 

 

Edited August 16 by Mordred