Talk:Momentum space

Convert page

This page is clearly only distantly related frquency domain. In my opinion this page should therefore be converted to its own seperate page. Unfortunately, I am not very well versed in the concept of momentum space, so I am requesting that someone else do it.

to do list

• a simple example could be added
• the math should be checked
• perhaps an analogy should be made to linear algebra where a change in basis is more intuitive.

--V. 18:06, 15 February 2007 (UTC)

Momentum eigenfunctions?

I just made an edit and undid it. The following is unclear to me:

$\psi (x)=\sum _{k}\phi _{k}\psi _{k}(x)$

First the page says that phi_k(x) are basis functions, then that psi_k(x) are. If I read this as a change of basis from x -> k, then phi_k is just the coefficient of psi in the k direction, and psi_k(x) is the coefficient of the psi_k basis vector in the x direction, no? So shouldn't we call psi_k (not psi_k(x)) the momentum eigenfunctions?

(Edit: on further thought, I guess one has to make explicit this dependence on x if one is writing in the position basis. I wonder if this can be made more clear though.) 76.93.124.92 (talk) 20:43, 14 July 2008 (UTC)

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How is the momentum operator what it is?

I've sat through 4 semesters on quantum mechanics and I still haven't seen the derivation that

${\hat {p}}=-i\hbar {\frac {d}{dx}}$

or any generalization thereof. What is the theoretical basis for this?--Loodog (talk) 19:26, 31 March 2009 (UTC)

This is how the momentum operator is defined. It can't be derived from theory. The reason it's called "momentum" is because in the classical limit it approaches the classical definition of momentum, which can be shown. Rckrone (talk) 21:14, 22 June 2009 (UTC)\

It is derived from the time derivative of the expectation value of the position. $<{\hat {p}}>=m{\frac {d<x>}{dt}}$

See Griffith Ch 1.5

k-space

It is my understanding that k-space is synonymous with momentum space. I'm most familiar with k-space being used in terms of reciprocal lattices in crystallography. Would it be wrong to mention in the introduction something like "momentum space, also known as k-space"? Larryisgood (talk) 17:26, 16 April 2011 (UTC)

Additionally, I would suggest providing a link to the page on crystallography Reciprocal lattice. 129.105.55.233 (talk) 15:27, 26 July 2011 (UTC)

Summation?

What is the relevance of linear combinations of discrete basis functions φ_k? Given that r and k are continuous vectors, only the integrals are needed... Delete the sums? It’s not like they introduce the reader to the concept of adding basis functions in the continuous way, they can see wavefunction and Schrödinger equation for how wavefunctions are sums of discrete bases and integrals of continuous basis... Maschen (talk) 08:28, 16 August 2012 (UTC)

Upgrade remainder of article to 3d

This can and should be done. I'll do it now. Maschen (talk) 08:36, 16 August 2012 (UTC)

Done. Maschen (talk) 08:58, 16 August 2012 (UTC)