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Field, Robert, 5.73 Introductory Quantum Mechanics I, Fall 2002. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed 09 Jul, 2010). License: Creative Commons BY-NC-SA

Introductory Quantum Mechanics I

Fall 2002

Time dependent Schrodinger equation for one spatial dimension. (Image courtesy of MIT OCW.)

Course Highlights

This course features comprehensive lecture notes on quantum mechanics, along with other materials used by students in the course.

Course Description

5.73 covers fundamental concepts of quantum mechanics: wave properties, uncertainty principles, Schrodinger equation, and operator and matrix methods. Basic applications of the following are discussed: one-dimensional potentials (harmonic oscillator), three-dimensional centrosymetric potentials (hydrogen atom), and angular momentum and spin. The course also examines approximation methods: WKB method, variational principle, and perturbation theory.

Technical Requirements

Mathematica® software is required to run the .nb files found on this course site.

The instructor would like to acknowledge Peter Giunta for preparing the original version of the materials for 5.73.

 Mathematica® is a registered trademark of Wolfram Research, Inc.


Robert W. Field
Recommended Text
Cohen-Tannoudji, Diu, and Laloë. Quantum Mechanics. Vols. 1 and 2.
Library Reserve Text
Merzbacher. Quantum Mechanics.
Tinkham. Group Theory and Quantum Mechanics.
Golding. Applied Wave Mechanics.
Condon, and Shortley. The Theory of Atomic Spectra.
Karplus, and Porter. Atoms and Molecules.
Three sessions / week
1 hour / session
One session / week
1 hour / session
  • Homework (weekly): 40% (~ten problem sets)
  • One Exam: 40% (open-book, take home)
  • In-Class Quizzes: 20% (approximately 30)

Tentative Exam Hand-in Date: Lecture 40

This is a course for users rather than admirers of Quantum Mechanics. It will wind its way,with a minimum of elegance and philosophical correctness, through a progression of increasingly complex (mostly) time-independent problems. We will begin with one-dimensional problems, treated in the Schrödinger Ψ(x) wavefunction picture. Then Dirac's bra-ket notation will be introduced and we will switch permanently to Heisenberg's matrix mechanics picture. In matrix mechanics all information resides in a collection of numbers called "matrix elements" and all sorts of trickery will be developed to find ways of deriving the values of all matrix elements without ever actually evaluating any integrals! One can never underestimate the importance of Perturbation Theory. Armed with matrices, we will turn to 3-D central force (spherical symmetry) problems, and discover that for all spherical systems (atoms), the angular factors of all matrix elements are trivially evaluable without approximation. Key topics are commutation rule definitions of scalar, vector, and spherical tensor operators, the Wigner-Eckart theorem, and 3-j (Clebsch-Gordan) coefficients. Finally, we deal with many-body systems, exemplified by many-electron atoms ("electronic structure"), anharmonically coupled harmonic oscillators ("Intramolecular Vibrational Redistribution: IVR"), and periodic solids.

The text is Quantum Mechanics, Volumes 1 and 2, by C. Cohen-Tannoudji, B. Diu, and F. Laloë (CTDL). The point of view of the text is quite different from the lectures (the text is more elegant, analytical, and logical). Reading assignments are intended to complement the lectures. Most homework, but few exam problems, will be based on the CTDL text. Additional reading material will be handed out in class, much of which is notes prepared almost 50 years ago by Professor Dudley Herschbach of Harvard University (while he was an Assistant Professor at Berkeley).

There will be approximately ten weekly problem sets, ~30 in-class 5-minute quizzes, and one take-home, open-book exam. A key difference between problems and the exam is that out-of-class discussion of the problems, but not of the exam, is expected. Problem sets should be handed in at the start of class on the specified due date and will be graded. Course grades will be determined by the average of the ten problem set grades (40%), the exam (40%) and approximately 30 in-class quizzes (20%). The quizzes are intended to exercise important concepts or techniques immediately after they are introduced.


This calendar provides the lecture topics for the course.


  LEC #       TOPICS  
  I. One Dimensional Problems  
  1       Course Outline. Free Particle. Motion?  
  2       Infinite Box, δ(x) Well, δ(x) Barrier  
  3       |Ψ(x,t)|2: Motion, Position, Spreading, Gaussian Wavepacket  
  4       Information Encoded in Ψ(x,t). Stationary Phase.  
  5       Continuum Normalization  
  6       Linear V(x). JWKB Approximation and Quantization.  
  7       JWKB Quantization Condition  
  8       Rydberg-Klein-Rees: V(x) from EvJ  
  9       Numerov-Cooley Method  
  II. Matrix Mechanics  
  10       Matrix Mechanics  
  11       Eigenvalues and Eigenvectors. DVR Method.  
  12       Matrix Solution of Harmonic Oscillator (Ryan Thom Lectures)  
  13       Creation (a ) and Annihilation (a) Operators  
  14       Perturbation Theory I. Begin Cubic Anharmonic Perturbation.  
  15       Perturbation Theory II. Cubic and Morse Oscillators.  
  16       Perturbation Theory III. Transition Probability. Wavepacket. Degeneracy.  
  17       Perturbation Theory IV. Recurrences. Dephasing. Quasi-Degeneracy. Polyads.  
  18       Variational Method  
  19       Density Matrices I. Initial Non-Eigenstate Preparation, Evolution, Detection.  
  20       Density Matrices II. Quantum Beats. Subsystems and Partial Traces.  
  III. Central Forces and Angular Momentum  
  21       3-D Central Force I. Separation of Radial and Angular Momenta.  
  22       3-D Central Force II. Levi-Civita. εijk.  
  23       Angular Momentum Matrix Elements from Commutation Rules  
  24       J-Matrices  
  25       HSO + HZeeman: Coupled vs. Uncoupled Basis Sets  
  26       |JLSMJ>↔ |LMLMS> by Ladders Plus Orthogonality  
  27       Wigner-Eckart Theorem  
  28       Hydrogen Radial Wavefunctions  
  29       Pseudo One-Electron Atoms: Quantum Defect Theory  
  IV. Many Particle Systems: Atoms, Coupled Oscillators, Periodic Lattice  
  30       Matrix Elements of Many-Electron Wavefunctions  
  31       Matrix Elements of One-Electron, F (i), and Two-Electron, G (i,j) Operators  
  32       Configurations and L-S-J "Terms" (States)  
  33       Many-Electron L-S-J Wavefunctions: L2 and S2 Matrices and Projection Operators  
  34       e2/rij and Slater Sum Rule Method  
  35       Spin Orbit: ζ(N,L,S)↔ζnl  
  36       Holes. Hund's Third Rule. Landé g-Factor via W-E Theorem.  
  37       Infinite 1-D Lattice I  
  38       Infinite 1-D Lattice II. Band Structure. Effective Mass.  
  39       Catch-up  
  40       Wrap-up   Tell A Friend