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fixed comments
author Robert McIntyre <rlm@mit.edu>
date Fri, 28 Oct 2011 04:56:15 -0700
parents 10c30f787f4b
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4:10c30f787f4b 6:b2f55bcf6853
360 \ldquo{}delta-normalizable \rdquo{} functions like these are included 360 \ldquo{}delta-normalizable \rdquo{} functions like these are included
361 among the physical wavefunctions. 361 among the physical wavefunctions.
362 362
363 363
364 364
365 * COMMENT: What I thought I knew 365 * COMMENT : What I thought I knew
366 366
367 The following is a list of things I thought were true of quantum 367 The following is a list of things I thought were true of quantum
368 mechanics; the catch is that the list contradicts itself. 368 mechanics; the catch is that the list contradicts itself.
369 369
370 1. For any hermitian operator: Eigenstates with different eigenvalues are orthogonal. 370 1. For any hermitian operator: Eigenstates with different eigenvalues are orthogonal.
402 realistic. Similarly, the energy operator no longer has an 402 realistic. Similarly, the energy operator no longer has an
403 eigenstate for each value of $E$; instead, the only energy 403 eigenstate for each value of $E$; instead, the only energy
404 eigenstates in the infinitely deep well 404 eigenstates in the infinitely deep well
405 are $E_n(x)=\sin(n\pi x/ a)$ for positive integers $n$. 405 are $E_n(x)=\sin(n\pi x/ a)$ for positive integers $n$.
406 406
407 * COMMENT: 407 * COMMENT :
408 408
409 ** Eigenstates with different eigenvalues are orthogonal 409 ** Eigenstates with different eigenvalues are orthogonal
410 410
411 #+begin_quote 411 #+begin_quote
412 *Theorem:* Eigenstates with different eigenvalues are orthogonal. 412 *Theorem:* Eigenstates with different eigenvalues are orthogonal.