Quantum Mechanics I
General Information
Syllabus
Lecture Schedule
Problem Sets
Instructor: Prof. Ivan Deutsch
Phys/Astro Room 24, Phone: 277-1502
email: ideutsch@unm.edu
Office Hours: Tuesday 10:00-11:00, room 30
Teaching Assistant: Anupam Mitra (anupam@unm.edu)
Office Hours: Tuesday 2:00-3:00, room TBA
Pre/co-requisites: Physics 330 and Math 314 (or equivalents)
Lectures: MW 1:00-2:15, PandA room 184
Problem Section: Friday 9:00-9:50, PandA room 184
Text (Required): None; Lecture Notes distributed via the website
Recommended texts: Introduction to Quantum Mechanics by D.J. Griffiths (2nd edition), A Modern Approach to QuantumMechanics by J. S. Townsend, Quantum Mechanics vol. 1 by C.. Cohen-Tannoudji et al.
Grading: • Problem Sets: 33.3% • Two Exams 66.7% (33.3% each)
Problem Sets: Available on Wednesday and due in one week on Wednesday in class. There will approximately 10 assignments throughout the semester.
Exam Dates:
Exam 1: Oct. 10., in class Exam 2: Dec. 5, in class
Exam 1: Oct. 10., in class
Exam 2: Dec. 5, in class
I Foundations A. Review - Historical overview, fundamental concepts. B. Mathematical foundation – Probability, statistics, waves and Hilbert space. C. Structure of quantum mechanics - States, observables, measurements, and dynamics.
II Waves Mechanics in 1D A. Wave function, momentum space, wave packets, Schrödinger equation. B. Bound states, one dimensional potentials, tunneling. C. Simple harmonic oscillator. D. Correspondence principle, Ehrenfest’s theorem.
III Beyond 1D Wave Mechancis A. Multiple degrees of freedoms. B. Wave mechanics in 1D, 2D, 3D. C. Angular momentum – spherical harmonics. D. Central potentials. E. The hydrogen atom. F. Scattering
Tentative Schedule of Lectures
Date
Topic
Notes
Aug. 20
Introduction to the strange world of quantum mechanics
Lecture 1
Podcast 1
Aug. 22
Quantum vs. classical probability: The Born rule
Lecture 2
Podcast 2
Aug. 27
Review: Probability and Statisitics
Lecture 3
Podcast 3
Aug. 29
Lecture 4
Podcast 4
Sep. 3
Labor Day: No Class
Sep. 5
Wave Mechanics: The Schrödinger equation
Lecture 5
Podcast 5
Sep. 11
Make up
Podcast 6
Sep. 12
Lecture 5a
Lecture 5b
Podcast 7
Sep. 17
Eigenfunctions, Eigenvalues,
Time Indepedent Schrödinger Equation
Lecture 6
Podcast 8
Sep. 19
The infinite square well, time dependent solutions, probability interpretation.
Lecture 7
Podcast 9
Sep. 24
Introduction to Hilbert Space,
Completeness, inner product, orthonormal functions
Lecture 8
Podcast 10
Continuation: Different representations in Hilbert Space
Podcast 11
Continuation: Hermitian Operators
Podcast 12
Oct. 3
The General Structure of Quantum Mechanics
States, Observables, Measurements, Dynamics
Lecture 9
Podcast 13
Oct. 5
Oct. 8
Continuation
Podcast 14
Oct. 10
Exam 1
Oct. 15
Generalized Measurement -- Quantum Bayes Rule
Lecture 10b
Podcast 15
Oct. 17
Compatible Observables - Commutators, Uncertainty Relations
Lecture 10
Generalized Uncertainty
Podcast 16
Oct. 22
Putting the mechanics in Quantum Mechanics
Ehrenfest Theorem
Lecture 11
Podcast 17
Oct. 24
1D Wave mechanics: General properties.
Bound vs. free energy levels. Symmetric finite square well.
Lecture 12
Podcast 18
Oct. 29
Bound states in 1D continued
Lecture 13
Podcast 19
Oct. 31
Podcast 20
Nov. 5
Parity, Symmetry, Double Well
Lecture 15
Podcast 21
Nov. 7
Tunnelling
Podcast 22
Nov. 12
Unbound States: Step potentials and barriers.
Scattering and Tunnelling.
Lecture 14
Podcast 23
Nov. 14
Simple Harmonic Oscillator
Introduction - Classical SHO, Phase Space, Units
Lecture 16
Podcast 24
Nov. 19
Solution to TISE for the SHO operator formulation
Lecture 17
Podcast 25
Nov. 21
Lecture 18
Podcast 26
Nov. 26
Podcast 27
Nov. 28
Dirac Notation Redux -- Postion, Momentum, Energy Representation
Podcast 28
Review
Podcast 29
Dec. 5
Problem Set #1
Problem Set 6
Problem Set #2
Problem Set 7
Problem Set 3
Problem Set 8
Problem Set 4
Problem Set 9
Problem Set 5
Problem Set 10