Physics 221A
Fall 2011
Notes 7
The WKB Method
1. Introduction
The WKB method is important both as a practical means of approximating solutions to the
Schrdinger equation, and also as a conceptual framework for understanding the classical limit of
o
quantu
Physics 221A
Fall 2011
Notes 1
The Mathematical Formalism of Quantum Mechanics
1. Introduction
The prerequisites for Physics 221A include a full year of undergraduate quantum mechanics.
In this semester we will survey that material, organize it in a more
Physics 221A
Fall 2011
Notes 16
Central Force Motion
1. Introduction
In these Notes we provide an introduction to central force motion, including the examples of
the free particle, the rigid rotor and diatomic molecules. In a later set of notes we will ta
Physics 221A
Fall 2011
Notes 17
Coupling of Angular Momenta
1. Introduction
In these notes we discuss the coupling or addition of angular momenta, a problem that arises
whenever dierent subsets of the degrees of freedom of a system, each possessing its ow
final.nb
1
Take-Home Final Exam
1. 3 d 2 p decays
(a)
In the electric dipole (E1) transitions, a photon is emitted in the J = 1 state, and hence only possible values of Jz of the photon are Jz = +, 0, -. The initial state has Jz = m = 2 . Suppose the fina
eigenvalues.nb
1
Solving Schrdinger equation numerically
Basic idea on working out the energy eigenvalues numerically is very simple. Just solve the Schrdinger equation with a guessed energy, and it always makes the wave function blow up at the infinity.
midterm.nb
1
1. n p 2 states
The purpose of this problem is to understand quantiatively the impact of the Coulomb repulsion among electrons in multi-electron atoms and the Hund's rule that picked a particular 2 S+1 LJ state as the ground state. We are not
221B Miscellaneous Notes on Contour Integrals
Contour integrals are very useful technique to compute integrals. For example, there are many functions whose indenite integrals cant be written in terms of elementary functions, but their denite integrals (of
221B Lecture Notes
Scattering Theory III
1
1.1
Partial Wave Analysis
Partial Wave Expansion
The scattering amplitude can be calculated in Born approximation for many
interesting cases, but as we saw in a few examples already, we need to work
out the scatt
221B Lecture Notes
Many-Body Problems I (Quantum Statistics) 1 Quantum Statistics of Identical Particles
If two particles are identical, their exchange must not change physical quantities. Therefore, a wave function (x1 , x2 , , xN ) of N identical partic
221B Lecture Notes
Many-Body Problems IV
Nuclear Physics
1
Nuclei
Nuclei sit at the center of any atoms. Therefore, understanding them is of central importance to any discussions of microscopic physics. Due to some reason, however, the nuclear physics had
Physics 221A
Fall 2011
Notes 19
Parity
1. Introduction
We have now completed our study of proper rotations in quantum mechanics, one of the important space-time symmetries. In these Notes we shall examine parity, another space-time symmetry.
In a latter s
Physics 221A
Fall 2011
Notes 15
Orbital Angular Momentum and Spherical Harmonics
1. Introduction
In Notes 13, we worked out the general theory of the representations of the angular momentum
operators J and the corresponding rotation operators. That theory
Physics 221A
Fall 2011
Notes 18
Irreducible Tensor Operators and the
Wigner-Eckart Theorem
1. Introduction
The Wigner-Eckart theorem concerns matrix elements of a type that is of frequent occurrence
in all areas of quantum physics, especially in perturbat
Physics 221A
Fall 2011
Notes 6
Topics in One-Dimensional Wave Mechanics
1. Introduction
In these notes we consider some topics that arise when solving the time-independent Schrdinger
o
equation for potential motion in one dimension. I have borrowed most o
Physics 221A
Fall 2011
Notes 5
Time Evolution in Quantum Mechanics
1. Introduction
In these notes we develop the formalism of time evolution in quantum mechanics, continuing the
quasi-axiomatic approach that we have been following in earlier notes. First
Physics 221A
Fall 2011
Notes 20
Time Reversal
1. Introduction
We have now considered the space-time symmetries of translations, proper rotations, and spatial
inversions (that is, improper rotations) and the operators that implement these symmetries on a
q
Physics 221A
Fall 2011
Notes 14
Spins in Magnetic Fields
1. Introduction
A nice illustration of rotation operator methods that is also important physically is the problem
of spins in magnetic elds. The earliest experiments with spins in magnetic elds were
Physics 221A
Fall 2011
Notes 12
Rotations in Quantum Mechanics, and
1
Rotations of Spin- 2 Systems
1. Introduction
In these notes we develop a general strategy for nding unitary operators to represent rotations
1
in quantum mechanics, and we work through
Physics 221A
Fall 2011
Notes 4
Spatial Degrees of Freedom
1. Introduction
In these notes we develop the theory of wave functions in conguration space, building it up
from the ket formalism and the postulates of quantum mechanics. We assume the particle ha
Physics 221A
Fall 2011
Notes 2
The Postulates of Quantum Mechanics
1. Introduction
In these notes we present the postulates of quantum mechanics, which allow one to connect
experimental results with the mathematical formalism described in Notes 1. Actuall
Physics 221A
Fall 2011
Notes 10
Charged Particles in Magnetic Fields
1. Introduction
An introduction to the quantum mechanics of charged particles in magnetic elds was given in
Notes 5. In these notes we examine several problems involving charged particle
Physics 221A
Fall 2011
Notes 21
Bound-State Perturbation Theory
1. Introduction
Bound state perturbation theory applies to the bound states of perturbed systems, for which the
energy levels are discrete and separated from one another. The system may also
221B Lecture Notes
Scattering Theory II 1 Born Approximation
| = | +
LippmannSchwinger equation 1 V | , (1) E H0 + i is an exact equation for the scattering problem, but it still is an equation to be solved because the state vector | appears on both sides
221B Lecture Notes
Many-Body Problems II
Atomic Physics
1
Single-Electron atoms
When there is only one electron going around a nucleus, it is a hydrogenlike atom: H, He+ , Li+ , Be3+ , etc. The energy levels of the electron is well-known, determined only
E $# [email protected] 8 p 1 S $ P k A F 8 # $ # 8 P 8 8 p { o $ A )v4GQ&QD6"(DS6Q'R% %QYvh(CQ)QCca)(Qv6a) A # 1 #$ P o y S 8 # 8 u #$ A D6TQ(D9eDv 06)Dfec0rt([email protected] 6)(0g { y { B ey (fr3{ y B c
E k B f k (X f (X ryk f 8 @C} )(k f k f h Yh k aE f k X k G(X f ah(X f YhX # P { { { $ # # P # 8 D (Qh(3%( (Q(gQ) o 1 { $ # { # i A 8 E B { $ F P 8A # F q Q6wR0&%TD'aqRh (GaRY@"k (
E $ F # # 5 5 # i # $ P 1 $ # S 8 S aQ(%)(4C@(a)R(%hQQR0"4Rj TQ()[email protected]& A S # A # S 8 # 8 5 8 # $ e)(63('a6Daha([email protected] )CRY)(4e@(| @RC(a7 E B i $ F P 8A# F ()[email protected]@V i 8 tQ0)
E
{ x
z mDR #%h 0$ # ht(taQCDC"Ra4@(%t D # P # g # # # g # $ #A g { x { x { ' mx e o # g A 8 #$ g A$ # A 1 #$ A j 8 DaQt(6fQ)ah60%G(0d(h6fQ)a# F o P 8 S g # n #$ a# 3 T(a
E B D } sn |{ t& rR 1 m # $ # # 8 # 8 # 8 e # #A h(a)ki) ~YQ)dz(l )ptQR)(h syDr } U tR E } z)E tR B } 6Df@()'Q D() l(5&DS } $ $ S e S S e # $ m 8 # # m # e # P 8 #$ A$ # ! ()@Y