I If an object is not quantized does it have a wave function?

[Nickyv2423]

Is there a relationship between the quantization of an object and its wave function? If an object isn't quantized does it have a wave function? For example, in string theory branes are not quantized, so do they have wave functions?

 

[hilbert2]

Objects are not quantized, measurable properties of objects can be. If you have an electron that is confined inside a finite space, its kinetic energy is quantized and can have only certain values. On the other hand, the kinetic energy of an unconfined free electron is not quantized. In both cases the state of the electron can be described with a wave function, but the free electron wavefunction doesn't have to be normalizable like the wavefunction of a confined electron.

 

[houlahound]

I take it a free electron does not have to be normalised because free electrons do not exist anywhere.

 

[DrClaude]

but the free electron wavefunction doesn't have to be normalizable like the wavefunction of a confined electron.

That's not correct. The wave function must always be normalizable, which is why a plane wave is not a valid state for an electron, and a superposition of plane waves (wave packet) is needed to correctly describe the state of a free particle.

 

[houlahound]

Not to be pedantic but is it correct to say a wave packet is not a free particle because it has to be in a potential to be in a superposition state.

Anyhoo good luck finding a region in the universe that is field free to support a free electron. Free particles seem mythical in the strict sense in my amateur opinion.

 

[Nugatory]

Anyhoo good luck finding a region in the universe that is field free to support a free electron. Free particles seem mythical in the strict sense in my amateur opinion.

It's easy to find free electrons: CRT displays, pre-flatscreen TV sets, vacuum tubes, lightning, static discharges... Electrons are so mobile that free electrons are responsible for almost all the transfers of electric charge that we see in daily life.

 

[Nugatory]

Not to be pedantic but is it correct to say a wave packet is not a free particle because it has to be in a potential to be in a superposition state.

Not correct. A particle is free if its total energy (kinetic plus potential) is positive when using the convention that the potential at infinity is zero.

Whether it's free or bound has nothing to do with superposition, and there is no such thing as a quantum state that is not a superposition in some basis.

 

[houlahound]

I have never seen a formal definition of free, I figured it must be free of all fields which excludes even weak fields relative the particles energy.

I guess you are saying an electron is free if it is ionised. Not trying to make up my own definitions but free is a pretty in accurate term the way you have defined it.

All electrons are in a gravity energy well at least, hence minimally bound.

Oh well my definition is wrong, I learned something.

If I was more adept I would like to calculate how gravity effects the spectra of a particle in a box problem, know any links for that?

BTW will start a separate thread re superposition.

 

[hilbert2]

That's not correct. The wave function must always be normalizable, which is why a plane wave is not a valid state for an electron, and a superposition of plane waves (wave packet) is needed to correctly describe the state of a free particle.

To put it more exactly, in the case of a confined electron, unnormalizable position repr. wavefunctions don't appear even as a mathematical tool in the eigenfunction expansions of the wavepackets.

 

[Demystifier]

It is possible to introduce a classical wave function in classical statistical physics:
https://arxiv.org/abs/quant-ph/0505143

 

[hilbert2]

It is possible to introduce a classical wave function in classical statistical physics:
https://arxiv.org/abs/quant-ph/0505143

That's quite cool... So the positivity of this classical wavefunction (mentioned in the abstract) prevents interference phenomena from happening in the classical case?

 

[Demystifier]

That's quite cool... So the positivity of this classical wavefunction (mentioned in the abstract) prevents interference phenomena from happening in the classical case?

Exactly!

 

[Mentz114]

That's quite cool... So the positivity of this classical wavefunction (mentioned in the abstract) prevents interference phenomena from happening in the classical case?

More precisely there cannot be interference because probabiity is assumed to follow normalised matter density $\rho$. The mapping from phase space to probability is not the same as in QT.