shminux comments on Which Basis Is More Fundamental? - Less Wrong

14 Post author: Eliezer_Yudkowsky 24 April 2008 04:17AM

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Comment author: Luke_A_Somers 21 October 2011 03:54:28PM *  1 point [-]

HY = EY is not the Schrödinger equation - it is the energy eigenstate equation. The Schrödinger equation is i ℏ ∂t[Y] = H Y.

(EDITED TO NOTE: Markdownr's sandbox renders the above correctly, but here it doesn't come through right.)

As you said, that's independent of basis. The Hamiltonian for a free spinless particle in momentum space is even more straightforward-looking than the hamiltonian in position space: k k / 2m + V(k). It doesn't even contain any explicit derivatives!

Of course, the V(k) contains the Fourier transform of the potential.

All in all, I'm split between agreeing with Eliezer on the primacy of position, and saying 'mu'.

Comment author: shminux 21 October 2011 05:25:28PM 0 points [-]

All in all, I'm split between agreeing with Eliezer on the primacy of position, and saying 'mu'.

Probably because the original post is actually a structureless rant. The only part that makes sense is

I accept the possibility that this whole blog post is merely stupid. After all, the question of whether the position basis or the momentum basis is "more fundamental" should never make any difference as to what we anticipate. If you ever find that your anticipations come out one way in the position basis, and a different way in the momentum basis, you are surely doing something wrong.

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