Lecture 3
April 5, 2013
Reading: Chapter 2
Problem Set #1 due Friday, April 12
1
1-D Waves on a String
L = n n / 2
n = 2L / n
n = 1, 2, 3, 4,
Quantized wavelength arising from boundary conditions.
2
1-D Infinite Square Well
V=
V=
V=0
0
V=
0 x L
Elsewhere
Physics 113A
Quantum Mechanics
Spring 2016
Problem Set 1
This problem set is due Friday 8 April at the start of discussion (10am). Late
problem sets delivered to [email protected] by Friday at 11:59pm will receive half
credit.
You may use Mathematica to he
Quantum Mechanics
Spring 2016
Problem Set 2
This problem set is due Friday 15 April at the start of discussion (10am). Late
problem sets delivered to [email protected] by Friday at 11:59pm will receive half
credit.
You may use Mathematica (or similar progr
Lecture 2
April 2, 4, 2013
Atomic Spectra
Hydrogen Atom Spectra
Bohr
Low Energy Electron
Reflection/Diffraction
Davisson & Germer
Si(100)
High Energy Electron Transmission/Diffraction
G.P. Thomson
TEM
Particle Tunneling
Tunneling:
-Particle
Decay
Tunneli
Problem 3.3
Suppose h|Qh = Qh|h for all functions h(x). Let h(x) = f (x) + cg (x) for some arbitrary constant c. Then
h|Qh = (f + cg )|Q(f + cg ) = f |Qf + c f |Qg + c g |Qf + |c|2 g |Qg ;
2
Qh|h = Q(f + cg )|(f + cg ) = Qf |f + c Qf |g + c Qg |f + |c| Qg
Problem #2
k ' tan k ' L
'
k
'
k cot k L
Even
k Odd
Let z=k ' L, z0 2 =2mV0 L2 / 2 , we can get
tan z
z0 z
cot z
In[3]:=
V0
In[4]:=
m
z0 z
13.6
9
In[39]:=
z0
1.6
1
Even
2
1
Odd
10 ^ 19;
10 ^ 32;
hbar
In[40]:=
2
1.05
10 ^ - 34;
Sqrt 2 m V0 L
hbar;
In[8]:=
Lecture 5
April 11, 2013
Orthogonality of Wavefunctions
+
m* n dx = 0
h2 d 2
+ V = E
2
2m dx
Suppose n and m are two wave functions with energies E n and Em
So:
h d n
+ V n = En n Eq. (1)
2
2m dx
2
2*
h d m
+ V *m = Em *m Eq. (2)
2m dx 2
2
2
Multiply Eq.
Name: Student ID:
Physics 113A Quantum Mechanics Spring 2013
9:30 10:50, RH 108, Thursday, April 25, 2013
Test #1
(Closed book. Calculator and one information sheet are allowed.)
All work is to be done within the exam pages.
Check that there are 14
John Gresl
75354960
Professor John Lowengrub
Due Date: Friday May 15 2015 at 5:00 PM
Lab Assignment 6
-Non-Linear Shooting Method
The goal of this lab is to develop a method to solve second order non-linear differential
equation. In this report, we will b