弘毅量子力学2016A1

武汉大学物理科学与技术学院 2016－2017(一)

《量子力学》课程期末考试试题 A 卷

学号： 姓名： 专业： 得分：

1. A particle of mass m in the half harmonic oscillator potential:

,

Please find the allowed energies(10 points)

2. Show that projection operator are idempotent:

, and then find the

eigenvalues and eigenvectors(10points).

3. Find the matrix representing S

for a particle spin 3/2 by using the basis of

one-dimensional infinite square well, find the energies and wave functions of

fermion ground state and next two excited states.(14 points)

5. Consider a three-dimensional vector space spanned by an orthonormal basis |1>,

|2>, |3>. Kets |α> and |β> are given by

(1). Construct bra <α| and <β|, (5 points)

(2). Find <α|β> and <β|α>, (5 points)

(3). Find matrix elements of the operator

. (5 points)

(2). Find the first three nonzero terms in the expansion of the correction to the

ground state (8 points)

7. The electron in a hydrogen atom occupies the combined spin and position state