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

Continuation: Different representations in Hilbert Space

  Oct. 1

Continuation: Hermitian Operators

 Oct. 3

The General Structure of Quantum Mechanics

States, Observables, Measurements, Dynamics

 Oct. 5

Exam I Review Session

Oct. 8

Continuation

 Oct. 10

Exam 1

 

 Oct. 15

Generalized Measurement -- Quantum Bayes Rule

 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

Parity, delta function potential

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

Continuation

 

 Nov. 26

Dirac Notation Redux -- Postion, Momentum, Energy Representation

 

 Nov. 28

Continuation

 
Dec. 3

Review

 

 Dec. 5

Exam 2
 

 


Problem Sets

 

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