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

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

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Article Navigation

Comments (37)
Tags: philosophy science

Comments (37)

Sort By: Old

You are viewing a single comment's thread. Show more comments above.

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: wnoise 21 October 2011 05:22:04PM *  1 point [-]

HY = EY is not the Schrödinger equation - it is the energy eigenstate equation.

Which is often called the time-independent Schrödinger equation. The one with the d/dt is then called the time-dependent Schrödinger equation.

Comment author: arundelo 21 October 2011 05:57:21PM 1 point [-]

Typo: one instance of "dependent" (the first, if I'm reading Wikipedia correctly) needs to be "independent".

Comment author: wnoise 22 October 2011 03:26:13AM 0 points [-]

Yep, fixing.

Comment author: Luke_A_Somers 02 November 2011 02:23:00PM 0 points [-]

What's that Lincoln quote about ducks and calling things?

Point is, Schrodinger's Equation contains within it an implication which leads to the energy eigenstate equation. Conflating the two is bad terminology, even if it's common. I would not call the force balance equation from statics "Newton's 2nd Law" - why should I do that in quantum mechanics, calling the Energy Eigenstate Equation "Schrodinger's Equation"? My more recent textbook goes out of its way to separate the two as it was found that conflating them was impeding students' understanding of quantum mechanics (though it does so in part by eliminating the term 'Schrodinger Equation' altogether).

Comment author: wnoise 02 November 2011 04:30:13PM 0 points [-]

That's an entirely reasonable argument that it shouldn't be called that.

But it is called that, and you have to be able to communicate with those who use it thus, or have it heard it this way, even while working to change the nomenclature.

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.

Powered by Reddit Powered by Reddit