The Medium of the QM Wave Function

[scuddyx]

What is the medium that the wave function oscillates in?

[Dagl1]

I have only a superficial understanding of this, so it may be wrong. But as far as I understand, there is no medium needed for particle/wave functions as they are not true waves. 
Or possibly, but again, this is just me guessing, the medium is the field(s) from which the particle(s) arise? 

Interesting question, hopefully the physicists around here will know!

[studiot]

 

1 hour ago, scuddyx said:

What is the medium that the wave function oscillates in?

The quantum wave function does not, in general, oscillate.

It has the units of metres^-0.5  and exists in a function space that is the Hilbert space of square integrable functions (in a state space of 1,2 or 3 dimensions)

Edit

In fairness the units I mentioned refer to the one dimensional case.

The wave function's units change according to how many dimensions you  are working in as it is the square root of a number divided by either a length or an area or a volume.

So it is really metre^-0.5 or metres^-1 or metres^-1.5 depending on this.

This is unlike the quantity mass which does not change units with number of dimensions (though density and volume  do)

 

The square integrable part allows the mathematics to form (and solve) the line, area or volume integrals

[math]\int {\Psi {\Psi ^*}} dx[/math]

[math]\int {\Psi {\Psi ^*}} dA[/math]

[math]\int {\Psi {\Psi ^*}} dV[/math]

as appropriate.

Edited January 16, 2020 by studiot

[swansont]

4 hours ago, scuddyx said:

What is the medium that the wave function oscillates in?

As Strange studiot says, in Hilbert space. 

It's a mathematical tool, so it seems reasonable that it exists in a mathematical space.

[Strange]

11 minutes ago, swansont said:

As Strange says, in Hilbert space.

Studiot. Who almost certainly knows what a Hilbert space is, unlike Strange.

[studiot]

11 minutes ago, Strange said:

Studiot. Who almost certainly knows what a Hilbert space is, unlike Strange.

 

[Strange]

15 minutes ago, studiot said:

 

Thanks. It turns out I did kind of know what it was then.

[scuddyx]

52 minutes ago, swansont said:

As Strange says, in Hilbert space. 

It's a mathematical tool, so it seems reasonable that it exists in a mathematical space.

The medium of sound waves are air molecules and the medium of ocean waves are water molecules.

Are you saying the medium of the wave function, whose evolution is described by the Schrödinger Equation, is pure maths (in Hilbert Space) or the medium is the field(s) from which the particle(s) arise as suggest by Dagl1?

Edited January 16, 2020 by scuddyx
added ()

[Mordred]

At the quantum level all particles are field excitations. These excitations do not require a medium nor eather to propogate.

 

[Strange]

1 hour ago, scuddyx said:

The medium of sound waves are air molecules and the medium of ocean waves are water molecules.

Are you saying the medium of the wave function, whose evolution is described by the Schrödinger Equation, is pure maths (in Hilbert Space) or the medium is the field(s) from which the particle(s) arise as suggest by Dagl1?

You can choose to think of the wave equation as a purely mathematical description in an abstract Hilbert space. Or you could choose to think of the field as the medium (but the field is just an abstract mathematical concept, so that isn't really much different from the first choice).

Perhaps the important point is that physics is not necessarily concerned with what things "really" are. In the case of water or sound waves, we have some sort of intuitive sense of what water or air "really" is (until you spend a bit of time in a philosophy class) so  it seems obvious what the waves really are.

In the case of quantum particles, all we have is a mathematical description that works. Whether it says anything about what these particles really are,  or whether a medium is needed, is all irrelevant. The only thing that matters is that the description works.

[swansont]

2 hours ago, Strange said:

Studiot. Who almost certainly knows what a Hilbert space is, unlike Strange.

Apologies to both of you.

1 hour ago, scuddyx said:

The medium of sound waves are air molecules and the medium of ocean waves are water molecules.

And molecules physically exist.

Quote

Are you saying the medium of the wave function, whose evolution is described by the Schrödinger Equation, is pure maths (in Hilbert Space) or the medium is the field(s) from which the particle(s) arise as suggest by Dagl1?

A wave function is a mathematical description of a phenomenon. Not the phenomenon itself. (An electron has a wave function. The electron is not itself a wave function). 

You are asking something akin to what medium comprises a probability (which is one aspect of what a wave function describes). It makes no sense to ask the question.

 

Wave functions and fields are related but still distinct concepts.

[studiot]

2 hours ago, scuddyx said:

The medium of sound waves are air molecules and the medium of ocean waves are water molecules.

Are you saying the medium of the wave function, whose evolution is described by the Schrödinger Equation, is pure maths (in Hilbert Space) or the medium is the field(s) from which the particle(s) arise as suggest by Dagl1?

And what is wrong with pure maths? (although this is applied)

I'm sure with you are happy with the idea of 3 apples.

But you couldn't go down to the greengrocers and but a 3.

3 is pure maths.

You could buy 1lb of apples but could you buy 1lb ?

You would no doubt be happy if I showed you a temperature distribution plot of the temperature in a pot of heated water.

But you couldn't grab the temperature from one point and stick it somewhere else.

 

Does this help?

 

54 minutes ago, swansont said:

3 hours ago, Strange said:

Studiot. Who almost certainly knows what a Hilbert space is, unlike Strange.

Apologies to both of you.

Not a problem.

Good joke actually.

[scuddyx]

On 1/16/2020 at 4:52 PM, studiot said:

And what is wrong with pure maths? (although this is applied)

I'm sure with you are happy with the idea of 3 apples.

But you couldn't go down to the greengrocers and but a 3.

3 is pure maths.

You could buy 1lb of apples but could you buy 1lb ?

You would no doubt be happy if I showed you a temperature distribution plot of the temperature in a pot of heated water.

But you couldn't grab the temperature from one point and stick it somewhere else.

 

Does this help?

 

Not a problem.

Good joke actually.

Are you saying the wave function (ψ) is just a number (a vector in Hilbert Space?) and a quantum mechanical operator is required to convert it into a physical quantity?

For instance, the expectation value of momentum <p> = ψ^*p^ ψ Where p^ = ih(bar)d/dx

Thanks

[swansont]

12 minutes ago, scuddyx said:

Are you saying the wave function (ψ) is just a number (a vector in Hilbert Space?) and a quantum mechanical operator is required to convert it into a physical quantity?

For instance, the expectation value of momentum <p> = ψ^*p^ ψ Where p^ = ih(bar)d/dx

Thanks

A QM operator doesn’t “convert it into a physical quantity”

The operator gives you a number, which represents the value. If you use the Hamiltonian you find the value of the energy, but you don’t actually get energy from that operation.

The information about the quantity is in the wave function.

[studiot]

5 hours ago, scuddyx said:

Are you saying the wave function (ψ) is just a number

No I said that the wave function has (rather peculiarly, but not uniquely)  unusual dimensions (or units).