Physics 491 Fall 2018

Quantum Mechanics I

UNMPhysics and Astronomy

 

Solvay Conference 1927

 


 

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General Information

Syllabus

Lecture Schedule

Problem Sets

 


General Information

 

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

 


Tentative Syllabus


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

Review of wave dynamics: Wave equation, superposition, wave packets, Fourier Transform.

Sep. 3

Labor Day: No Class

 

 Sep. 5

Wave Mechanics: The Schrödinger equation

Sep. 10
No Class: Travel

Sep. 11

Make up

Momentum space, the uncertainty principle.

 Sep. 12

The uncertainty principle - Measurement backaction

Lecture 5a

Lecture 5b

Podcast 7

 Sep. 17

Eigenfunctions, Eigenvalues,

Time Indepedent Schrödinger Equation

Sep. 19

The infinite square well, time dependent solutions, probability interpretation.

 Sep. 24

Introduction to Hilbert Space,

Completeness, inner product, orthonormal functions

 Sep. 26

The General Structure of Quantum Mechanics

States, Observables, Measurements, Dynamics

 
 

Compatible Observavbles -

Commutators, Uncertainty, Conservation Laws

 

 Oct. 1

Putting the mechanics in Quantum Mechanics

Ehnrenfest Theorem, Classical Trajectories

 

 Oct. 3

1D Wave mechanics: General properties.

Bound vs. free energy levels. Symmetric finite square well.

 

Oct. 8

Bound states in 1D continued

Parity, delta function potential.

 

 Oct. 10

Exam 1

 

 Oct. 15

Unbound states -- Scattering
 

 Oct. 17

Unbound States: Step potentials and barriers.

Tunnelling.

 

  Oct. 22

Simple Harmonic Oscillator -- Introduction

Classical review and quantization.

 

 Oct. 24

Solution to TISE for the SHO, analytic formulation

 

 Oct. 29

SHO: Wave functions in position and momentum space.

 

 Oct. 31

Wave mechanics in 3D - separation of coordinates.

 

 Nov. 5

Central potentials - radial and angular momentum, radial and angular Schrödinger equation.

 

 Nov. 7

Angular momentum in quantum mechanics: spherical harmonics, operator algebra, and commutation relations.

 

Nov. 12

Spherical Wells.

 

Nov. 14 

Two-body central force problem: Hydrogen atom. 

 

Nov. 19

Hydrogen eigenvalue problem

 

Nov. 21

Hydrogen: Energy spectrum, eigenfunctions, etc.

 

 Nov. 26

Scattering - Unbound problems in 3D

 

 Nov. 28

Low Energy Scattering - Partial Wave Expansion
 
Dec. 3

 

Review

 

 Dec. 5

Exam 2
 

 


Problem Sets

 

Problem Set #1

 

Problem Set #2

 

Problem Set 3

 

Problem Set 3