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5.73

Introductory Quantum Mechanics I

3-0-9 units · Graduate

Presents the fundamental concepts of quantum mechanics: wave properties, uncertainty principles, Schrodinger equation, and operator and matrix methods. Includes applications to one-dimensional potentials (harmonic oscillator), three-dimensional centrosymetric potentials (hydrogen atom), and angular momentum and spin. Approximation methods include WKB, variational principle, and perturbation theory.

Fall 2018 · Quantum Mechanics I

Topics

  • Course Outline; Free Particle; Motion?
  • Infinite Box, \(\delta(x)\) Well, \(\delta(x)\) Barrier
  • \({\mid{\Psi(x,t)}\mid}^2\): Motion, Position, Spreading, Gaussian Wavepacket
  • Stationary Phase and Gaussian Wavepackets
  • Continuum Normalization
  • Linear \(V(x)\); JWKB Approximation and Quantization
  • JWKB Quantization Condition
  • Rydberg-Klein-Rees: \(V(x)\) from \(E_{vJ}\)
  • Numerov-Cooley Method: 1-D Schrödinger Equation
  • Matrix Mechanics
  • Eigenvalues, Eigenvectors, and Discrete Variable Representation (DVR)
  • Matrix Solution of Harmonic Oscillator
  • End of Matrix Solution of H-O, and Feel the Power of the a and a † Operators
  • Perturbation Theory I; Begin Cubic Anharmonic Perturbation
  • Perturbation Theory II; Cubic and Morse Oscillators
  • Perturbation Theory III; Transition Probability; Wavepacket; Degeneracy
  • Perturbation Theory IV; Recurrences; Dephasing; Quasi-Degeneracy; Polyads
  • Variational Method
  • Density Matrices I; Initial Non-Eigenstate Preparation, Evolution, Detection
  • Density Matrices II; Quantum Beats; Subsystems and Partial Traces
  • 3-D Central Force Problems I; Separation of Radial and Angular Momenta
  • 3-D Central Force Problems II; Levi-Civita \(\varepsilon_{ijk}\)
  • Angular Momentum Matrix Elements from Commutation Rules
  • J-Matrices
  • H SO + H Zeeman : Coupled vs. Uncoupled Basis Sets
  • H SO + H Zeeman in ⎜JLSM J \(\rangle\) and ⎜LM L M S \(\rangle\) by Ladders plus Orthogonality
  • Wigner-Eckart Theorem
  • Hydrogen Radial Wavefunctions
  • Begin Many e - Atoms: Quantum Defect Theory
  • Matrix Elements of Many-Electron Wavefunctions
  • Matrix Elements of One-Electron, \(F(i)\), and Two-Electron, \(G(i,j)\) Operators
  • Configurations and Resultant L-S-J “Terms” (States)
  • L-S Terms via L 2 , S 2 and Projection
  • \(e^2/r_{ij}\) and Slater Sum Rule Method
  • Spin Orbit: Many Electron ζ(N,L,S)↔Single Orbital ζ\(_{nl}\) Coupling Constants
  • Holes; Hund’s Third Rule; Landé g-Factor via W-E Theorem
  • Infinite 1-D Lattice I
  • Infinite 1-D Lattice II; Band Structure; Effective Mass
  • One-Dimensional Lattice: Weak-Coupling Limit

Readings

  • Cohen-Tannoudji, C., B. Diu, and F. Laloë. Quantum Mechanics . Vol. 1. Wiley-VCH, 1st edition, 1992. ISBN: 9780471569527.
    Listed reading
  • Cohen-Tannoudji, C., B. Diu, and F. Laloë. Quantum Mechanics . Vol. 2. Wiley-VCH, 1st edition, 1991. ISBN: 9780471164357.
    Listed reading
  • The readings assigned for selected lectures are listed below. Readings were mostly assigned from the course textbook, unless indicated otherwise.
    Listed reading
  • [C-T,D,L-1] = Cohen-Tannoudji, C., B. Diu, and F. Laloë. Quantum Mechanics . Vol. 1 (pp.1-891). Wiley-VCH, 1st edition, 1992. ISBN: 9780471569527.
    Listed reading
  • [C-T,D,L-2] = Cohen-Tannoudji, C., B. Diu, and F. Laloë. Quantum Mechanics . Vol. 2. (pp.901-1517). Wiley-VCH, 1st edition, 1991. ISBN: 9780471164357.
    Listed reading
  • Ses #: 2 · topics: Infinite Box, \(\delta(x)\) Well, \(\delta(x)\) Barrier · readings: [C-T,D,L-1] pp. 21–24, 28–31.
    Reading assignment
  • Ses #: 5 · topics: Continuum Normalization · readings: [C-T,D,L-1] pp. 103–107, [C-T,D,L-2] pp. 1468–76.
    Reading assignment
  • Ses #: 9 · topics: Numerov-Cooley Method: 1-D Schrödinger Equation · readings: [C-T,D,L-1] pp. 94–121.
    Reading assignment
  • Ses #: 10 · topics: Matrix Mechanics · readings: [C-T,D,L-1] pp. 121–144.
    Reading assignment
  • Ses #: 13 · topics: End of Matrix Solution of H-O, and Feel the Power of the a and a † Operators · readings: [C-T,D,L-1] pp. 488–508.
    Reading assignment
  • Ses #: 14 · topics: Perturbation Theory I; Begin Cubic Anharmonic Perturbation · readings: [C-T,D,L-2] pp. 1095–1107, 1110–1119.
    Reading assignment
  • Ses #: 18 · topics: Variational Method · readings: [C-T,D,L-2] pp. 1148–1155, [C-T,D,L-1] pp. 252–263, 295–307.
    Reading assignment
  • Ses #: 19 · topics: Density Matrices I; Initial Non-Eigenstate Preparation, Evolution, Detection · readings: [C-T,D,L-1] pp. 153–163, 199–202, 290–294.
    Reading assignment
  • Ses #: 20 · topics: Density Matrices II; Quantum Beats; Subsystems and Partial Traces · readings: [C-T,D,L-1] pp. 643–652.
    Reading assignment
  • Ses #: 22 · topics: 3-D Central Force Problems II; Levi-Civita · readings: [C-T,D,L-1] pp. 643–660.
    Reading assignment
  • Ses #: 27 · topics: Wigner-Eckart Theorem · readings: [C-T,D,L-2] pp. 999–1085, especially pp. 1048–1053.
    Reading assignment
  • Ses #: 29 · topics: Begin Many-Electron Atoms: Quantum Defect Theory · readings: Ross, Stephen. “ MQDT Primer ” pp. 73–110 in Half Collision Resonance Phenomena in Molecules (AIP Conf. Proc. #225, M. Garciá-Sucre, G. Raseev, and S.C. Ross) 1991. DOI: https://doi.org/10.1063/1.40550 ↗
    Reading assignment
  • Ses #: 36 · topics: Holes; Hund’s Third Rule; Landé g-Factor via W-E Theorem · readings: [C-T,D,L-2] pp. 1156–1178.
    Reading assignment
  • Ses #: 37 · topics: Infinite 1-D Lattice I · readings: [C-T,D,L-2] pp. 1156–1168.
    Reading assignment
  • Baym, Gordon. Lectures on Quantum Mechanics . Benjamin Cummings Publishing Company, 1969. ISBN: 9780805306675.
    Listed reading
Fall 2005

Topics

  • Perturbation Theory

Readings

  • Cohen-Tannoudji, C., F. Laloë, and B. Diu. Quantum Mechanics . Vols. 1 and 2. New York, NY: John Wiley & Sons, 2006. ISBN: 9780471569527.
    Recommended
  • Shankar, R. Principles of Quantum Mechanics . 2nd ed. New York, NY: Springer-Verlag, 1994. ISBN: 9780306447907.
    Listed reading
  • Sakurai, J. J. Modern Quantum Mechanics . Boston, MA: Addison-Wesley, 1994. ISBN: 9780201539295.
    Listed reading
  • Karplus, Martin, and Porter. Atoms and Molecules . Boston, MA: Addison-Wesley, 1970. ISBN: 9780805352184.
    Listed reading

Prerequisites & course information

Prereq: 5.611 , 5.612 , 8.03 , and 18.03 G (Fall) 3-0-9 units

Sources