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Department of Physics and Astronomy The McMahon Group

Physics 550 & 551: Quantum Theory I & II

 

The following are a series of lecture notes that I wrote and used to teach Physics 550 (Quantum Theory I) during the Fall of 2016 at WSU. A few quick words:

  • This course takes a very non-traditional approach: less axiomatic; and “derives” quantum theory from a historical perspective …
  • … yet: it is fully rigorous; and presents all of the content of a traditional graduate-level course.
  • These notes make extensive use of mathematics.
  • In class, there were supplemental mathematical lectures, but they are not (yet?) posted here.
  • Many supplemental examples were presented in class, but they are not (yet?) posted here.

 

Note: Prior to beginning, it would be helpful to review the following (below):

  • Classical mechanics
  • Mathematical prerequisites

 

0. Introduction

Lecture 0-1. Introduction to quantum mechanics

Lecture 0-2. Towards a quantum theory

 

1. Old quantum theory

Lecture 1-1. Spectral lines

Lecture 1-2. Atomic models

Note: At this point, it would be helpful to review Fourier series (below).

Lecture 1-3. Bohr’s model of the atom

Lecture 1-4. The interaction between matter and radiation

Lecture 1-5. Passage to quantum theory

 

2. Matrix mechanics

Lecture 2-1. Heisenberg’s reinterpretation4

Lecture 2-2. Introduction to matrix mechanics (Born and Jordan)5

Note: At this point, it would be helpful to review Fourier matrices (classical and quantum) (below).

Lecture 2-3. (Quantum) Hamiltonian mechanics

Lecture 2-4. The quantization condition

Lecture 2-5. The rules of quantum theory (1925)

Lecture 2-6. The law of commutation

Note: At this point, it would be helpful to review commutators (below).

Lecture 2-7. The Heisenberg equation of motion

Lecture 2-8. The energy theorems

Lecture 2-9. Integrating the canonical equations

 

3. The formulation of quantum mechanics

Lecture 3-. Mechanical aspect

Lecture 3-. Dynamical variables

Lecture 3-. Statistical aspect

Lecture 3-. Statistical interpretation

Lecture 3-. Quantum states

Lecture 3-. State operator

Lecture 3-. States

Lecture 3-. The state operator as an operator

 

4. Symmetry

Lecture 4-. Symmetries in quantum mechanics

Lecture 4-. Wigner’s theorem

Lecture 4-. Mapping of operators

Lecture 4-. Continuous symmetries

Lecture 4-. Active vs. passive transformations

 

5. Kinematics and dynamics

Lecture 5-. Galilean group

Lecture 5-. Time in quantum mechanics

Lecture 5-. “Pictures” of quantum mechanics

 

Lecture 4-. Quantization rules

 

5. Representations

Lecture -. Arbitrary representations

Lecture -. The coordinate representation

  • Schroedinger equation

Lecture -. The momentum representation

 

7. Angular momentum

Lecture -. The coordinate representation

Lecture -. Spherical harmonics

Lecture -. Example: hydrogen atom

 

8. Time-dependent phenomena

Lecture -. Example: the ammonia molecule

 

9. Measurement in quantum mechanics

Lecture -. State preparation and determination

Lecture -. Measurement

Lecture -. Example: Stern–Gerlach experiment

 

10. Summary

Lecture -. Postulates of quantum mechanics

 


 

Wave Mechanics 

The hydrogen-like atom

 


 

Review of classical mechanics

Lecture -. Newtonian mechanics

Lecture -. Principle of stationary action

Lecture -. Lagrangian mechanics

Lecture -. Hamiltonian mechanics

 


 

Mathematical prerequisites

Lecture -. Linear vector spaces

Lecture -. Linear operators

Lecture -. Eigenvalues and eigenvectors

Lecture -. Probability theory

 


 

Other mathematics (and mathematical physics)

Fourier series and Fourier series in mechanics

Fourier matrices

Note: The audio for the last two drawings of Fourier matrices are in another lecture.

(Quantum) Fourier matrices

Matrix calculus

Binomial coefficient

 


 

Supplemental Reading

Note: The following links direct you to external websites, where you can access the documents.

  1. A. Einstein, “Concerning an Heuristic Point of View Toward the Emission and Transformation of Light,” Ann. Physik 17, 132 (1905) [Translation]
  2. N. Bohr, “On the Quantum Theory of Line-spectra,” in Memoirs de l’Academie Royale des Sciences et des Lettres de Danemark, Copenhague (1918)
  3. M. Born, “Quantum Mechanics,” Zs. f. Phys. 26, 379–395 (1924)
  4. W. Heisenberg, “Quantum-theoretical Re-interpretation of Kinematic and Mechanical Relations,” Zs. Phys. 33, 879–893 (1925)
  5. M. Born and P. Jordan, “On Quantum Mechanics,” Zs. f. Phys. 34, 858–888 (1925)
  6. M. Born, W. Heisenberg, and P. Jordan, “On Quantum Mechanics II,” Zs. Phys. 35, 557–615 (1926)
  7. P. A. M. Dirac, “The Fundamental Equations of Quantum Mechanics,” Proc. Roy. Soc. A 109, 642–653 (1926)
  8. M. Born, “The statistical interpretation of quantum mechanics,” Nobel lecture (1954)

 

  1. M. F. Pusey, J. Barrett, and T. Rudolf, “On the reality of the quantum state,” Nature Physics 8, 475–478 (2012)

 

Problem Sets

Problem Set 1    | Answers

Problem Set 2.1 | Answers

Problem Set 2.2 | Answers

Problem Set 2.3 | Answers

Problem Set 3    | Answers

Problem Set 4    | Answers

Problem Set 5    | Answers

Problem Set 6    | Answers

Problem Set 7    | Answers

 

In-class Activities

Quiz 1

Quiz 2

Ex: Principle of Correspondence

 

Exams

Midterm | Answers

Final | Answers

Midterm (551) | Answers

 


 

Other

Syllabus (550)

Syllabus (551)