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I need some help with three multiple choice questions 1. Imagine a particle of e

ID: 3900628 • Letter: I

Question

I need some help with three multiple choice questions


1.

Imagine a particle of energy E in a square

well potential of depth V0:

The solution for SE in range x>a is

described by the following equation:

A)?(x)=Ae^(-Kx)+Be^(+Kx)

B)?(x)=Ae^(-Kx)

C)?(x)=Be^(+Kx)

D)?(x)=Ae^(ikx)+Be^(-ikx)

E)?(x)=Ae^(ikx)

(note: both A and B could be nonzero)


2.Consider a hermitian operator Q, and two wavefunctions A and B,

such that A=QB

Both wave functions are expressed as vectors in a complete orthonormal

basis of wave functions |e> and are denoted as |?> and |?>, respectively:

A=??|e> =|?> B=??|e> =|?>

In that case a matrix Q could be found that the following linear matrix

transformation is true: |?>=Q|?>


A) Always true

B) True only if basis |en> represents egenfunctions of Hamiltonian

C) It is not true



3. Assuming that ? is the solution for time independent Schr

Explanation / Answer

1. B) since it has to decay to zero as x-> infinity

2. B)

3. b) since a is the lower operator decrases i in energy