General Information
Syllabus
Lecture Schedule
Problem Sets
Exam
Instructor: Prof. Ivan Deutsch
Phys/Astro Room 24, Phone: 277-1502
email: ideutsch@info.phys.unm.edu
Office Hours: Thursday : 2:00-3:00 and Friday: 9:00-10:00 (or by appointment)
Teaching Assistant: Andrew Sliberfarb
email: drews@unm.edu
Problem Session: Thursday 4:30-5:30, Physics Reading Room (190)
Grading:
Problem Sets: 25-33%
Problem sets will be distributed once a week on the web on Friday and due in one week, to be placed in the grader's mailbox by 3:00 PM.
Two Take-Home "Midterms" 50-66%
Exam I Oct. 7-9, Exam II Nov. 20-22
Final Exam (optional oral) 25%
"Recommended" Texts:
We will not be following any text directly. Copies of my lecture note will be available. The are many good texts out there; you should pick the one(s) that work best for you. Relevant material from the following recommended texts with be referenced throughout the course.
o Quantum Mechanics , vol. I and II, by C. Cohen-Tannoudji, B. Diu, and F. Laloë.
This text is a great reference book to have around, but very verbose and sometimes hard to wade through. Many classic problems are solved in the "Complements.
o Modern Quantum Mechanics, by J. J. Sakurai
Good advanced text with a modern perspective. It's somewhat terse, are there are few examples.
o Quantum Mechanics 3rd Edition, by E. Merzbacher
Every thing is here but in the organization is difficult. This is a new edition and contains many contemporary topics.
Other texts:
o Quantum Mechanics, by L. I. Schiff
The old advanced classic. Still a good reference. Somewhat old fashion
o Quantum Mechanics, vol. I and II, by A. Messiah
Another older classic and good reference
Quantum Mechanics , vol. I, by K. Gottfried.
Recently republished. Contains a reasonable coverage of measurements theory.
o Introductory Quantum Mechanics, R. L. Liboff
An upper division undergraduate text . Very clear.
I Foundations (4 weeks)
A. Mathematical foundation - Hilbert space, operators, eigenvalues, commutators.
B. Structure of quantum mechanics - States, observables, measurements.
C. Quantum dynamics - Schrödinger and Heisenberg pictures, conservation laws.
II Waves Mechanics in 1D (3 1/2 weeks)
A. Wave function, momentum space, wave packets, Schrödinger equation.
B. Bound states, one dimensional potentials, tunneling.
C. Correspondence principle, Ehrenfest's theorem, WKB.
D. Simple harmonic oscillator - Different representations, phase space in QM.
III Angular Momentum (3 weeks)
A. Angular momentum as the generator of rotations, commutation algebra.
B. Eigenstates, Spherical harmonics.
C. Spin and magnetic resonance.
IV Multiple Degrees of Freedom (4 1/2 weeks)
A. Entangled states, Einstein-Podolsky-Rosen paradox.
B. Addition of angular momentum - Clebsch-Gordan coefficients.
C. Wave mechanics in 3D.
D. Central potentials.
E. The hydrogen atom.
Tentative Schedule of Lectures
Date
Topic
Notes
Aug. 19
Introduction to quantum notions - probability amplitude, wave/particle duality
Download 1
Aug. 21
Math: Linear vector spaces, representations, inner product, Dirac notation
Download 2
Aug. 26
Math: Operators, adjoints, change of basis, unitarity
Download 3
Aug. 28
Math: Eigenvalues, eigenvectors, commutators
Download 4
Sept. 2
Labor Day
No Class
Sept. 4
Math: Hermitian operators, Complete sets of commuting operators
Postulates of quantum mechanics- States, observables
Download 5
Sept. 9
Postulates of quantum mechanics- Dynamics:
Unitary reversible evolution vs. Nonunitary irreversible evolution
Download 6
Sept. 11
Pure vs. mixed states - density operators
Download 7
Sept. 16
No Lecture: (Yom Kippor)
Sept. 18
Quantum Dynamics:
Time evolution operator, conservation, and symmetries
Stationary-states: Time Independent Schrödinger Equation
Sept. 23
Time evolution: Schrödinger vs. Heisenberg
Download 9
Sept. 25
Particle mechanics in 1D, Heisenberg picture,
x and p representations.
Download 10
Sept. 30
Infinite dimensional Hilbert space continued
Oct. 2
Wave mechanics, interpretation of the wave function:
Probability current, semiclassical limit.
Download 11
Oct. 4
No Homework Due
Oct. 7
Time Independent Schrödinger Equation (TISE).
Free particle, scattering states, constant potentials
Exam I Distributed
Download 12
Oct. 9
Parity, bound states
Exam I Due
Download 13
Oct. 14
SHO, Review classical problem, a and a^\dag
Oct. 16
SHO, Energy eigenstates, x-p space
Download 15
Oct. 21
(Out of town - to be made up)
Oct. 23
SHO, coherent states and phase space
Download 16
Oct. 28
Eigenvalue problem for angular momentum
Download 18
Oct. 30
Oribtal angular momentum and spherical harmonics
Download 19
Nov. 4
Interaction of charge particle and magentic field:
Para and diamagentism
Download 20
Nov. 6
Spin angular momentum
Download 21
Nov. 11
Many degrees of freedom - Tensor product structure
Download 22
More on tensor product:
Separability, entangled states, marginal density operator
Nov. 18
Addition of angular momentum
Coupling of two spins: Singlet and triplet
Download 23
Nov. 20
Solutions to Schrödinger equation for multiple degrees of freedom -
Separability, degeneracy, and symmetry
Download 24
Nov. 25
Lecture Canceled
Exam. II Distributed
Nov. 27
Exam. II Due
Nov. 28
THANKSGIVING
Dec. 2
Dec. 4
Central potential -
Separation in spherical coordinates and the radial equation
Hydrogen and hydrogenic atoms
Download 25
Download 26
Download 27
Dec. 7-14
EPR, Hidden Variables, and Bell Inequalties
Download 28
Diagnostic
Problem Set #1
Due Aug. 30
Problem Set #6
Due Oct. 18
Problem Set #11
Due Dec. 6
Problem Set #2
Due Sept. 6
Problem Set #7
Due Oct. 25
Problem Set #3
Due Sept. 13
Problem Set #8
Due Nov. 1
Problem Set #4
Due Sept. 20
Problem Set #9
Due Nov. 8
Problem Set #5
Due Sept. 30
Problem Set #10
Due Nov. 19
Exams
Practice Exam 2, 1998 and Solutions
Practice Exam 2, 2000 and Solutions