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conantee
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 « on: December 31, 2009, 10:05:20 AM »

18. The wavefunction , where and are real constants, is a normalized eigenfunction of the Schrodinger equation for a particle of mass and energy in a one dimensional potential such that at . Which of the following is correct?
(A)
(B)
(C)
(D)
(E)
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conantee
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 « Reply #1 on: December 31, 2009, 10:26:29 AM »

First, energy of eigenstates does not depend on x-coordinate, so (D) is wrong.
Next, we can obtain the dimension of energy from schrodinger's equation. The kinetic energy term is . So, the dimension of energy is . Well, from the wave function , has dimension of . Hence, dimension of energy in (E) is wrong.
Next, we know that at , so (A) is also wrong.

Now, let's think about Schrodinger equation for eigenstates.
.
We can plug and find . However, full calculation is not necessary. Since the kinetic energy term involves with just second derivative, there is no coming from Gaussian function. So, (C) is wrong.

The correct is therefore (B). 30 of 100 people got the correct answer.
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