Quantum Mechanics
Mathematical Structure
and
Physical Structure
Problems and Solutions
John R. Boccio
Professor of Physics
Swarthmore College
April 9, 2012
Contents
3
Formulation of Wave Mechanics - Part 2
3.11 Solutions . . . . . . . . . . . . . . . . .
Intermediate QMI
Ch 4 Problem Solutions
Problem 4.4
1
Given a beam of spin- 2 particles of speed v0 passing through a series of two SGz devices. The first transmits particles with
Sz = 2 and filters out particles with Sz = - 2, whereas the second transmit
Introduction to Quantum Mechanics I,Fall 2014
Solution for chapter 7 assignment
7.7
Since
is the superposition of n 0 and n 1
c1 0 c2 1
2
c1
1
2
2
c2
1
1
1 i
0
e 1
2
2
2
px px
( 0
1
1 i
m
1
1 i
1
e )(i
)(a a )(
0
e 1)
2
2
2
2
2
i (e i e i ) m
m
Introduction to Quantum Mechanics I,Fall 2014
Solution for chapter 6 assignment
6.1
(a)
Suppose [ x , p x ] in' x
n'
n ' 1
holds for n' n
When n' n 1 ,
[ x n 1 , p x ] x[ x n , p x ] [ x, p x ]x n
i nx n i x n
i(n 1) x n
So [ x , p x ] in' x
n'
Introduction to Quantum Mechanics I,Fall 2014
Solution for chapter 5 assignment
5.1
2A
H 2 S1
S 2 0 S1z
2A
2 ( S1x S 2 x S1 y S 2 y S1z S 2 z ) 0 S1z
A/ 2
1
1
A/ 2
A
0
A
A/ 2
1
2
A / 2
1
A 0
0
0
0
2
A 0
0
A
0
2
A 0
0
A
Introduction to Quantum Mechanics I,Fall 2014
Solution for chapter 4 assignment
4.5
B B0 sin i B0 cos k
B gq S B
H
2mc
0 (sin S x cos S z )
0 1
Sx
2 1 0
1 0
Sz
2 0 1
cos
H 0
2 sin
sin
cos
The eigenstates of H :
cos
det 0
sin
2
sin
0
Introduction to Quantum Mechanics I,Fall 2014
Solution for chapter 3 assignment
3.2
S n S n sin cos S x sin sin S y cos S z
In S z basis according to equ (3.77),(3.88),(3.89)
0
sin cos
0
Sn
2 i sin sin
0
2 sin cos
0 cos sin e i
cos
cos
Introduction to Quantum Mechanics I,Fall 2014
Solution for chapter 2 assignment
2.10
First represent S x in x , x
basis.
Since S x x x , S x x x
2
xS x
x
Sx
xS x
x
2
x Sx x
x
x Sx
1 0
2 0 1
U represents the unitary operator.(similar to (2.99)
Introduction to Quantum Mechanics I,Fall 2014
Solution for chapter 1 assignment
1.2
We set the origin of the coordinate in the center of the ball as showed in fig1 below.
z
i
r
Fig1
All the characters used are illustrated above. represents the angular ve
.model small
.data
arr db 10 dup(?)
.code
start:
mov ax , @data
mov ds , ax
lea si , arr
mov di , si
mov cl , 10
;scan 10 numbers
l:
mov ah, 01h
int 21h
mov [si] , al
inc si
loop l
;logic of bubble sort
mov si , di
mov bp , si
mov cl , 10
fori:
mov bh , c