Quiz 2
15 minutes; Probability ux 1. [4 points] The Schrdinger equation is i real potential, as usual.
t (x, t)
2
Phys 139A, Spring 2008, UC Santa Cruz
= 2m x2 (x, t) + V (x)(x, t) where V (x) is a
2
j (a) Show the derivation of the following continuity
Quiz 1 + Math/Physics Questionnaire
25 mins; closed-everything [not even looking up tables, for this one]
April 10, 2008
Phys 139A, Spring 2008, UCSC
1. [Quiz 5 points] Consider a wave of light with angular frequency
energy
E.
impinging on your eye, depos
What we learned so far by doing QM
UCSC,
139A,
G.-H.
Spring
Sam
2008
Gweon
Answers given below are basic guides, and you are asked to provide your own
answers, when the guide is simply that and does not give the final answer
explicitly.
1. Time
dependent
Some Guide to the Final Exam
(Monday, June 9, 4-6 PM; Optionally till later; Classroom)
UCSC,
Phys
139A,
Gey-Hong
1. Couple
of
important
topics
that
were
harmonic oscillator and free particle).
of
the
continuum
problems
2. The
[HW
parity
stationary
readin
L12 IDENTICAL PARTICLES, PERTURBATION, AND ENTANGLEMENT
UCSC, PHYS 139A, SPRING 2008
GEY-HONG SAM GWEON
Two Particles
1.
For two particles, the spatial wave function should be written as
(x1 , x2 , t)
If we include the spin wave function (spinor), it can
L11 ANGULAR MOMENTUM
UCSC, PHYS 139A, SPRING 2008
GEY-HONG SAM GWEON
1.
Orbital Angular Momentum
From CM, we are familiar with the following denition of the angular momentum
L=rp
In QM, we dene angular momentum operators accordingly
Lx = y pz z py , Ly =
L10 THE HYDROGEN PROBLEM
UCSC,
PHYS
139A,
GEY-HONG
1.
SPRING
SAM
2008
GWEON
Radial Equation
Applying the potential
V (r ) =
the radial equation for
u(r)
becomes
2
(1.1)
e2 1
4 0 r
d2 u(r)
l(l + 1)
+
2
2m dr
2mr2
2
e2 1
u(r) = Eu(r)
4 0 r
E < 0 only (boun
L10 THE HYDROGEN PROBLEM - ADDENDUM FOR DETAILED ALGEBRA
UCSC,
PHYS
139A,
GEY-HONG
SPRING
SAM
2008
GWEON
Here are the derviations of the details of the radial equation for the hydrogen problem. The big
picture of how things are handled is more important t
L9 THE HYDROGEN PROBLEM RICH PREVIEW
UCSC, PHYS 139A, SAM SPRING 2008 GEY-HONG GWEON
1. Bohr-Sommerfeld Quantization Rule Before we do QM, let us do some quantization and if you rule. have This to rule should between
semi-classical
be viewed semi-classica
Major changes are described. Small changes are not mentioned.
All changes are marked by blue characters in the pdf file.
May 20, 2008
- Page 20: Axiom 5.2: Continuum case is better described.
- Page 21, top: Some words about "wave function collapse".
- Pa
L8 FORMALISM OF QUANTUM MECHANICS
UCSC, PHYS 139A, SPRING 2008
GEY-HONG SAM GWEON
This note is quite lengthy. I suggest a quick browsing, a topical reading, and then a full reading,
if you still have time. For the topical reading, the following informatio