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conantee
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 « on: January 08, 2010, 02:11:46 AM »

96. A particle of mass is an infinitely deep square well potential where
for and
for

A very small perturbing potential is superimposed on such that
for  and
for

If are the energy eigenfunctions for a particle in the infinitely deep square well potential, with being the ground state, which of the following statements is correct about the eigenfunction of a particle in the perturbed potential ?
(A)
(B) with for all odd values of
(C) with for all even values of
(D) with for all values of
(E) None of the above
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 « Reply #1 on: October 16, 2010, 11:49:14 AM »

This question is difficult for who do not know perturbation theory. However, you can eliminate (D) and (E) since they are not famous for correct answers (no thinking, no relation with symmetry of perturbed potential). (A) is also wrong since scaling old ground state wave function yields same ground state energy - not the new perturbed ground state energy. Now, you can guess between (B) and (C).

Actually, the coefficient is equal to . Since is even function and , the ground state of a particle in a infinite square well, is even, needs to be odd so that becomes zero. As a result, we needs to be odd to make .

The correct answer is therefore (B). 23 of 100 people answered this question correctly.
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