Talk:Fock state

Hi, I'm happy you're working to improve the physics Wikipedia. However I have some problems with your changes ( I used to use this page as a reference all the time ).

1) Please cite a source that anyone can verify and is well know. Fock states are in many condensed matter theory physics text books. The lecture notes are not well known and may have errors.

2) Proof read! There are errors on this page now and I can't trust it any more " We can generate any multimode Fock state from vacuum state by operating it by Creation operator: (equation) " is wrong, confusion of indices. This again might be a problem in the source.

3) finally, don't assume everyone reading the page understands advanced mathematics, by all means include proofs, but you shouldn't have to read the proofs and follow them to use fock states.

I think you can fix these things, I don't have time right now to do it all myself and again, I'm happy you're working on this. Rydbergite (talk) 17:11, 6 November 2014 (UTC)

Answers to your doubts

I'm sorry about the confusions. Here I'm answering to your problems:

1) Apart from the lecture note, I have mentioned, I have referred to five more books, which you can easily verify. I have verified every single topic I have included from various sources I have mentioned, and only after being sure about it, I edited that part.

2) Thanks for pointing this out. I think I have understood what you wanted to mean. I had to use these indices because the page was written using these kind of indices before me. Taking, $k_{1}=\alpha$, $k_{2}=\beta$, etc. might reduce the confusion. And by using the term 'vacuum state' I wanted to mean that there is no particle in any of the energy states. I think this clears the confusion. (If it doesn't please, let me know.)

3) Wherever, I thought it needs a proof I have supplied it. If you think any of the statements, need proof, please let me know. I shall add the proof right away.

Thank you very much for pointing out facts which needed clarifications. I hope I could clarify the doubts. If you still have any, please let me know. Indranil1993 (talk) 13:57, 8 November 2014 (UTC)

Editing the Article

Hi all, I want to edit this article on Fock state. My plan of editing has five steps:

• In the wikipedia page, I want to start from editing the definition of Fock state. I want to add that, Fock states are those kets of Fock space, which are eigenkets of number operator. And mathematical formalism of constructing Fock state by denoting occupation number of a state, and hence action of number operator on a general Fock state will be shown. And this will work as the formal definition of a Fock state.
• In the next part, I want to add a new section under heading Example using 2 particles. There, I am planning to show that even if the Fock state of 2 particles is symmetric or antisymmetric under exchange of kets of individual particles, action by a number operator gives the same result.
• In the next part, I want to add another section under heading Bosonic Fock state. In that part by calling the fock states corresponding to symmetric behaviour of the state due to action of exchange operator, as bosonic fock states; action of creation and annihilation operators on that state will be shown. And hence action of number operator will be shown.
• In the next part, in a new section under heading Fermionic Fock state: by calling the fock states corresponding to antisymmetric behaviour of the state due to action of exchange operator, as fermionic fock states; action of creation and annihilation operators, as well as, of number operator will be shown. Further, after proving using Slater determinant that number of particles in each of the states can be either 0 or 1 for a fermionic fock state, it will be shown that action of creation and annihilation operators will be different from that of bosonic fock states. And that action of number operator will give either 0 or 1 as eigenvalues, will also be shown. (Hence a link to Pauli exclusion principle can be mentioned.)
• The portion in wikipedia under the heading Energy eigenstates: is not true. If the system consists of non-interacting particles, then the Hamiltonian can be shown to commute with particle number operator. On the other hand, if the particles interact among themselves, then the Hamiltonian does not not commute with the particle number operator. So this portion can be edited and the reason of fock states, not being energy eigenstates, will be added.

Any suggestion and discussion and question on my plan is always welcome. Please do ask if you have any doubt. I shall try to explain as far as I can. You can visit my page to know the resources I will be using till I update this page. Indranil1993 (talk) 17:51, 15 October 2014 (UTC)

Most of this article is covered in second quantization

I think it might make more sense to merge any new content from this page into second quantization and put a redirect from here to that article instead of duplicating a bunch of information. What does everyone else think? Natsirtguy (talk) 23:33, 11 December 2014 (UTC)

We certainly need the page on a Fock state as an example of a non-classical state, but we do not need to duplicate the second quantization article.--Ymblanter (talk) 06:56, 12 December 2014 (UTC)

Subsection called "Operation by a Number operator" is unneeded

This section purports to deduce something fundamental about bosons and fermions, namely that we cannot tell them apart just using the number operator, but it's not clear that anything substantive has really been said, since our hypotheses haven't been spelled out clearly enough to see that they are distinct from the conclusion.

I thought of deleting this subsection.

What I did instead was shorten it and merge it with the previous section. But it still seems a bit out of place. 178.38.89.67 (talk) 19:47, 25 April 2015 (UTC)

Why k_i ?

Throughout the article, k_i is written, for example:

$|n_{{\mathbf {k} }_{1}},n_{{\mathbf {k} }_{2}},....n_{{\mathbf {k} }_{m}}...n_{{\mathbf {k} }_{l}}...\rangle$.

Since the basis of the underlying space is fixed the whole time, can't we systematically shorten k_i to i when it is used as a subscript, e.g.

$|n_{1},n_{2},...,n_{m},...,n_{l},...\rangle$

?

178.38.89.67 (talk) 19:55, 25 April 2015 (UTC)

$|n_{k_{1}},n_{k_{2}},...\rangle =\prod \limits _{i=1}^{\infty }{\frac {(b_{k_{i}}^{+})^{n_{k_{i}}}}{\sqrt {n_{k_{i}}!}}}|0,0,...\rangle .$

What is the expectation value of a ?

Consider this text from the article:

The vacuum state or $|0\rangle$ is the state of lowest energy and the expectation values of $a$ and $a^{\dagger }$ vanish in this state:

$a|0\rangle =0=\langle 0|a^{\dagger }$

My question: How can a or a^† have an "expectation value"? They are not self-adjoint operators (not observables).

For example, a^†|0> is not zero, yet <0|a^†|0> = 0. This would make no sense for an observable.

178.38.89.67 (talk) 20:13, 25 April 2015 (UTC)

Still, the expectation values can be formally defined. They are non-zero for these operators, for example, in a coherent state.--Ymblanter (talk) 20:20, 25 April 2015 (UTC)

So the expectation of a general operator yields a complex value, that is fine. But what is its interpretation of this formal value? It does not appear, for example, in the article Expectation value (quantum mechanics), where only self-adjoint operators are considered. Should I think of a general operator as just a complex-valued observable? That is not too bad, I guess. Maybe it is common. But perhaps there is a link or reference that explains this.

In any case, I would have to think in what sense a is an observable, what it is measuring. In any case we can see what a^†a is measuring. That makes the remark in the article quite interesting. 178.38.89.67 (talk) 22:19, 25 April 2015 (UTC)

Yes, it is generally a complex-valued quantity. It can not be measured (all measurable operators are hermitian), but it sometimes simplifies the interpretation.--Ymblanter (talk) 22:32, 25 April 2015 (UTC)