Classical vs. Quantum Harmonic Oscillator (split)

[swansont]

1 hour ago, Kartazion said:

Isn't this standing wave the entire location of the photon?

No. Waves are waves and particles are particles. 

You can have a hydrogen atom that's just of order 0.05 nanometer in radius (the most probable electron distance, i.e. Bohr radius) and yet it will absorb light that's several hundred nanometers in wavelength. The wavelength is not the location of the photon. You can't equate the two. 

[Kartazion]

I was talking about a localization of the photon in relation to the standing wave. But if this standing wave is not represented by the photon, what does this standing wave represent?

[swansont]

3 minutes ago, Kartazion said:

I was talking about a localization of the photon in relation to the standing wave.

As was I

3 minutes ago, Kartazion said:

But if this standing wave is not represented by the photon, what does this standing wave represent?

It's the distribution of the electric and magnetic field, to name two things. The classical wave.  

 

[Kartazion]

1 hour ago, swansont said:

As was I

It's the distribution of the electric and magnetic field, to name two things. The classical wave.  

Ok.

What is the role and the implication of the second quantization in all that we just said in this thread? It another method of to be able to determine the localization of the particle? Or a standardization of the field in a classical and quantum entity?

Edited July 1, 2021 by Kartazion

[swansont]

I'm not the right one to ask. Never did delve much into field theory and second quantization.

[Kartazion]

3 hours ago, swansont said:

It's the distribution of the electric and magnetic field, to name two things. The classical wave.  

I understand that the photon trapped in the cavity is detected by its electric and magnetic field.

[swansont]

11 minutes ago, Kartazion said:

I understand that the photon trapped in the cavity is detected by its electric and magnetic field.

Usually it's detect by being absorbed somewhere, or having some other interaction. What method are you alluding to here?

[Kartazion]

17 minutes ago, swansont said:

What method are you alluding to here?

 

A photon trappe in an optical resonator coupled with two-level atoms.

[swansont]

3 hours ago, Kartazion said:

 

A photon trappe in an optical resonator coupled with two-level atoms.

I recall experiments where you can have the excited atom or a photon, but that isn’t detecting the fields. That’s absorbing the photon.

[Kartazion]

On 2/12/2020 at 12:02 PM, swansont said:

The momentum-position version of the HUP tells you that the particle has no definite location.

On 2/12/2020 at 1:07 PM, Kartazion said:

I understand. The particle is localized by a probability distribution.

On 2/12/2020 at 2:53 PM, swansont said:

Right. It's in a region, but you don't have a specific location, just limits on where it might be found.  

 

What is the name of this region determined by the probability of wave function and defined by their respective field? We already know that the particle is found in this region.
 

On 2/12/2020 at 5:56 PM, swansont said:

Yes. If by "trap" you mean in an optical cavity — put the radiation in a cavity so you have a standing wave, it just sits there, but you can't localize where the photon would be. That's true for anything with a wave nature.

Would this standing wave would have the same name of this region spoken previously?
 

3 hours ago, swansont said:

I recall experiments where you can have the excited atom or a photon, but that isn’t detecting the fields. That’s absorbing the photon.

I admit that the example of the photon is not the simplest in our example. The cavity quantum electromagnetics  is drifting into a utility of quantum computer and optical quantum communication. I even understand in itself that no photon is emitted, but simply the use of an oscillation of the electron at the level of their energy between two intermediate n shells.

[swansont]

13 hours ago, Kartazion said:

What is the name of this region determined by the probability of wave function and defined by their respective field? We already know that the particle is found in this region.

As far as I recall, there’s no particular name. In many cases, the region is all space.

[Kartazion]

6 hours ago, swansont said:

As far as I recall, there’s no particular name. In many cases, the region is all space.

This appears to be a 'Zone of localized disturbances of the fields of action'. This corresponds to the particle as well as its constituent annex components.

My question is now whether there is an equation or a unification formalism of the wave function with the electromagnetic field?

Thanks again.

PS: The proportionality between probability density for a harmonic oscillator and the volume density of electromagnetic energy, must be linked.
 

[swansont]

24 minutes ago, Kartazion said:

constituent annex components.

I have no idea what you mean by this

[Kartazion]

15 minutes ago, swansont said:

I have no idea what you mean by this

Auxiliary components of the particle like EM wave.

There is an equation or a unification formalism of the wave function with the electromagnetic field?

Finally I created a new thread related to the Unification between the Probability Density of the particle and the Energy Density of an electromagnetic wave

[swansont]

33 minutes ago, Kartazion said:

Auxiliary components of the particle like EM wave.

An EM wave isn’t a component of a particle

33 minutes ago, Kartazion said:

There is an equation or a unification formalism of the wave function with the electromagnetic field?

In my part of physics you can use the “dressed state” approach

Particle wave function has ground and excited states, with numbers of particles in each, and photon states have an occupation number. The photons and atoms can interact.

https://www.quora.com/What-are-dressed-states-in-Quantum-Optics

[Kartazion]

25 minutes ago, swansont said:

An EM wave isn’t a component of a particle

Ok. But we agree that what field theory does best is localize the particle in relation to its fields.

[swansont]

9 minutes ago, Kartazion said:

Ok. But we agree that what field theory does best is localize the particle in relation to its fields.

No, “we” don’t.

Dressed state formulation, for example, uses energy eigenstates. No localization. Position isn’t an eigenstate.

[Kartazion]

On 7/2/2021 at 2:49 AM, Kartazion said:

What is the name of this region determined by the probability of wave function and defined by their respective field? We already know that the particle is found in this region.

On 7/2/2021 at 4:15 PM, swansont said:

As far as I recall, there’s no particular name. In many cases, the region is all space.
 

On 7/2/2021 at 11:20 PM, Kartazion said:

This appears to be a 'Zone of localized disturbances of the fields of action'. This corresponds to the particle as well as its constituent annex components.
 

 

 

I found Fock space. I don't know the scope and actual use of Fock space in current physics. The intervention of the second quantification becomes inevitable insofar as it partially responds to the OP with the coherent states.

Partial Wikipedia summary:

The Fock space is an algebraic construction used in quantum mechanics to construct the quantum states space of a variable or unknown number of identical particles from a single particle Hilbert space H. Informally, a Fock space is the sum of a set of Hilbert spaces representing particle(s). If the identical particles are bosons, the n-particle states are vectors in a symmetrized tensor product of n single-particle Hilbert spaces H. If the identical particles are fermions, the n-particle states are vectors in an antisymmetrized tensor product of n single-particle Hilbert spaces H. A Fock state or number state is a quantum state that is an element of a Fock space with a well-defined number of particles (or quanta). Fock states play an important role in the second quantization formulation of quantum mechanics.

In quantum mechanics, a coherent state is a quantum state of a quantum harmonic oscillator whose behavior resembles that of a classical harmonic oscillator.

The theory describing the coherent states involves the operator annihilation and creation of the second quantization. From the definition of the operator displacement, one can derive that a coherent state corresponds to the superposition of states of Fock.

Creation and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. In many subfields of physics and chemistry, the use of these operators instead of wavefunctions is known as second quantization.

[swansont]

28 minutes ago, Kartazion said:

I found Fock space. I don't know the scope and actual use of Fock space in current physics. The intervention of the second quantification becomes inevitable insofar as it partially responds to the OP with the coherent states.

Fock space is not a physical region. The “space” is a mathematical one. There was a recent discussion of this

[Kartazion]

22 minutes ago, swansont said:

Fock space is not a physical region. The “space” is a mathematical one. There was a recent discussion of this

The Fock space is defined as the Hilbert space obtained by the direct sum of the tensor products of the Hilbert spaces for a particle. Hilbert's concept of space extends the methods of linear algebra by generalizing the notions of Euclidean space.

It's a question, but isn't Euclidean space a projection of the reality and a description of the object in a physical space?

[swansont]

16 hours ago, Kartazion said:

The Fock space is defined as the Hilbert space obtained by the direct sum of the tensor products of the Hilbert spaces for a particle. Hilbert's concept of space extends the methods of linear algebra by generalizing the notions of Euclidean space.

It's a question, but isn't Euclidean space a projection of the reality and a description of the object in a physical space?

I can talk of things in momentum space, which is not spatial. Describing things of x,y,z is one option, but not the only one.