【免费】弘毅量子力学2018A1资源-CSDN文库

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武汉大学物理科学与技术学院 2018－2019(一)

《量子力学》课程期末考试试题 A 卷

学号：姓名：专业：得分：

1. (15 points) Show that two noncommuting operators can not have a complete set of

common eigenfunctions.

2. (16 points) A particle of mass m in the infinite square well has the initial wave

function:

� �

a

x

A

a

x

Ax

��

�

53

sin4-sin50, �

,

determine A(4 points), find

� �

tx,

�

(8 poingts),and calculate the expectation value

of the energy(4 points).

3. (16 points)Construct the angular momentum matrices (

zyx

JJJ

ˆ

,

ˆ

,

ˆ

) and

2

ˆ

J

for a system of

angular quantum number

2

3

�

j

.

4. (18 points) Find the allowed three lowest energies of two-noninteracting particles

in the infinite square well, and obtain these wavefunctions,

�

�

�

�

��

�

otherwise

ax

xV

00

)(

,

(a). distinguishable particles without spin(6 points);

(b). identical bosons with spin 1(6 points);

(c). identical fermions with spin 1/2(6 points).

5. (20 points) The three dimensional rotation Hamiltonian is

3

2

2

2

1

2

222

I

L

I

L

I

L

H

z

y

x

��

,

find the energy for ground state:

(a).

IIII

��

321

(5 points);

(b).

IIIII

2,

321

��

(5 points);

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