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8.04

Quantum Physics I

5-0-7 units. REST · Undergraduate

Experimental basis of quantum physics: photoelectric effect, Compton scattering, photons, Franck-Hertz experiment, the Bohr atom, electron diffraction, deBroglie waves, and wave-particle duality of matter and light. Introduction to wave mechanics: Schroedinger's equation, wave functions, wave packets, probability amplitudes, stationary states, the Heisenberg uncertainty principle. Solutions to Schroedinger's equation in one dimension: transmission and reflection at a barrier, potential wells, delta functions, the simple harmonic oscillator. Schroedinger's equation in three dimensions: central potentials and the hydrogen atom. Introduction to spin-1/2.

Spring 2016

Topics

  • Introduction: Basic features of quantum mechanics: Linearity, complex numbers, nondeterministic, superposition, entanglement.
  • Two-slit experiments. Mach-Zehnder interferometer. Elitzur-Vaidman bombs.
  • Photoelectric effect. Compton Scattering. de Broglie wavelength.
  • Galilean transformation of de Broglie wavelength. Wave-packets and group velocity.
  • Matter wave for a particle. Momentum and position operators. Schrödinger equation.
  • Interpretation of the wavefunction. Probability density, probability current. Current conservation. Hermitian operators.
  • Expectation values of ˆx. Wave-packets and uncertainty. Time evolution of wave-packets. Shape changes. Fourier transforms and Parseval Theorem.
  • Momentum expectation values. General definition of expectation values of Hermitian operators. Time derivative of expectation values (Ehrenfest theorem). Commutators.
  • Hermitian operators as observables: Real eigenvalues orthogonal eigenfunctions. Measurement postulate. Uncertainty defined. Uncertainty relation stated.
  • Stationary states. Boundary conditions for the wavefunction. Particle on a circle.
  • Infinite square well. Basic properties of one-dimensional potentials. The finite square well.
  • Turning points, semiclassical approximations, qualitative features of the wavefunction.
  • Numerical solution by the shooting method.
  • Delta function potential. Discussion of the node theorem. Setup for the simple harmonic oscillator: Differential equation.
  • Analysis of the differential equation: Hermite polynomials. Algebraic solution of the harmonic oscillator with creation and destruction operators.
  • Scattering states continued. Reflection and transmission coefficients. Constructing wave packets. Finding a particle in the forbidden region?
  • Ramsauer Townsend effect. Finite square well, resonant transmission. Scattering in 1D by finite range potentials.
  • 1D Scattering and phase shifts. Example. Levinson’s theorem.
  • Resonances and Breit-Wigner distribution. The complex k-plane
  • Central Potentials and Angular momentum. Algebra of angular momentum. Simultaneous eigenstates of L z and L 2 . Legendre polynomials.
  • QAssociated Legendre polynomials. Radial equation. Begin Hydrogen atom. 2-body problem and separation of variables.
  • Scales in the hydrogen atom. Differential equation: behaviors at infinity and at zero. Series solution. Energy quantization.
  • Energy levels diagram for hydrogen. Virial theorem applied. Circular orbits and eccentricity.
  • More on orbits and turning points. The simplest quantum system and discovering spin

Readings

  • Griffiths, David J. Introduction to Quantum Mechanics . Pearson Prentice Hall, 2004. ISBN: 9780131118928.
    Required
  • Shankar, Ramamurti. Principles of Quantum Mechanics . Plenum Press, 1994. ISBN: 9780306447907. (A conceptual textbook with many superb explanations.)
    Listed reading
  • Cohen-Tannoudji, et al. Quantum Mechanics, Vols. 1 & 2 . Wiley, 1991. ISBN: 9780471164333 and 9780471164357. (Useful for this course as well as for Quantum Physics II and III. Many students find it too encyclopedic.)
    Listed reading
  • Liboff, Richard L. _Introductory Quantum Mechanic_s. Addison Wesley, 2002. ISBN: 9780805387148. (A detailed and pedagogic textbook with many exercises.)
    Listed reading
  • Gasiorowicz, Stephen. Quantum Physics . Wiley, 2003. ISBN: 9780471057000. (Efficient textbook, with plenty of material but little explanation.)
    Listed reading
  • Dirac, Paul Adrien Maurice. The Principles of Quantum Mechanics . Clarendon Press, 1982. ISBN: 9780198520115. (Deep, hard and rewarding. Not practical during the semester.)
    Listed reading
  • Ohanian, Hans C. Principles of Quantum Mechanics . Prentice Hall, 1989. ISBN: 9780137127955.
    Listed reading
Spring 2013

Topics

  • Introduction to Superposition
  • Experimental Facts of Life
  • The Wave Function
  • Expectations, Momentum, and Uncertainty
  • Operators and the Schrödinger Equation
  • Time Evolution and the Schrödinger Equation
  • More on Energy Eigenstates
  • Quantum Harmonic Oscillator
  • Operator Methods for the Harmonic Oscillator
  • Clicker Bonanza and Dirac Notation
  • Dispersion of the Gaussian and the Finite Well
  • The Dirac Well and Scattering off the Finite Step
  • More on Scattering
  • Resonance and the S-Matrix
  • Eigenstates of the Angular Momentum Part 1
  • Eigenstates of the Angular Momentum Part 2
  • More on Central Potentials
  • “Hydrogen” and its Discontents
  • Identical Particles
  • Periodic Lattices Part 1
  • Periodic Lattices Part 2
  • Metals, Insulators, and Semiconductors
  • More on Spin
  • Entanglement: QComputing, EPR, and Bell’s Theorem

Readings

  • Eisberg, Robert M., and Robert Resnick. Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles . Wiley, 1985. ISBN: 9780471873730.
    Required
  • Liboff, Richard L. Introductory Quantum Mechanics . Addison Wesley, 2002. ISBN: 9780805387148.
    Required
  • Gasiorowicz, Stephen. Quantum Physics . John Wiley & Sons, 2003. ISBN: 9780471429456.
    Required
  • Shankar, Ramamurti. Principles of Quantum Mechanics . Springer, 2008. ISBN: 9780306447907.
    Required
  • Dirac, Paul Adrien Maurice. The Principles of Quantum Mechanics . Clarendon Press, 2011. ISBN: 9780198520115. A beautiful text, strongly recommended.
    Required
  • Griffiths, David J. Introduction to Quantum Mechanics . Upper Saddle River, Pearson Prentice Hall, 2005. ISBN: 9780131118928. [Preview with Google Books ] A very popular undergraduate text. ↗
    Required
  • Feynman, Richard P., Robert B. Leighton, and Matthew L. Sands. The Feynman Lectures on Physics . Addison Wesley, 1989. ISBN: 9780201500646. Read again and again.
    Required
  • Albert, David Z. Quantum Mechanics and Experience . Harvard University Press, 1994. ISBN: 9780674741133. [Preview with Google Books ] Chapters 1–3 provide an elegant introduction for philosophers; avoid the later chapters. ↗
    Required
  • [E&R] = Eisberg, Robert M., and Robert Resnick. Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles . Wiley, 1985. ISBN: 9780471873730.
    Listed reading
  • [Li.] = Liboff, Richard L. Introductory Quantum Mechanics . Addison Wesley, 2002. ISBN: 9780805387148.
    Listed reading
  • [Ga.] = Gasiorowicz, Stephen. Quantum Physics . John Wiley & Sons, 2003. ISBN: 9780471429456.
    Listed reading
  • [Sh.] = Shankar, Ramamurti. Principles of Quantum Mechanics . Springer, 2008. ISBN: 9780306447907.
    Listed reading
  • [E&R] Chapter 1: Sec. 6 and 7; Chapter 2: Sec. 1, 2, 3, 4, and 5; Chapter 3: all.
    Listed reading
  • [Li.] Chapter 1: all; Chapter 2: Sec. 3, 5, and 6.
    Listed reading
  • [Ga.] Chapter 1: Sec. 2, 3, and 4.
    Listed reading
  • [Sh.] Chapters 3 and 1.
    Listed reading
  • [E&R] Chapter 3: all; Chapter 5: Sec. 1, 3, 4, and 6.
    Listed reading
  • [Li.] Chapter 2: Sec. 5–8; Chapter 3: Sec. 1–3.
    Listed reading
  • [Ga.] Chapter 2: all except 4.
    Listed reading
  • [Sh.] Chapters 3 and 4.
    Listed reading
  • [E&R] Chapter 5: all
    Listed reading
  • [Li.] Chapter 3: Sec. 1–3; Chapter 5: Sec. 2–4.
    Listed reading
  • [Ga.] Chapter 2: all; Chapter 3: Sec. 2.
    Listed reading
  • [Sh.] Chapters 1 and 4.
    Listed reading
  • [E&R] Chapter 5: all, Chapter 6: Sec. 1, 2, and 8.
    Listed reading
  • [Li.] Chapter 3: all; Chapter 4: Sec. 1; Chapter 5: Sec. 1; Chapter 6: all.
    Listed reading
  • [Ga.] Chapter 2: Sec. 4; Chapter 3: all.
    Listed reading
  • [Sh.] Chapter 4: all; Chapter 5: Sec. 1 and 2.
    Listed reading
  • [E&R] Chapter 6: Sec. 9, App. I.
    Listed reading
  • [Li.] Chapter 7: Sec. 1 and 4.
    Listed reading
  • [Ga.] Chapter 4: Sec. 7; Chapter 6: Sec. 1 and 2.
    Listed reading
  • [Sh.] Chapter 6: all; Chapter 7: all.
    Listed reading
  • [E&R] Chapter 6: all; App. G, H.
    Listed reading
  • [Li.] Chapter 7: Sec. 1–9; Chapter 8: Sec. 1.
    Listed reading
  • [Ga.] Chapter 4: all; Chapter 5: all; Chapter 6: Sec. 1 and 2.
    Listed reading
  • [Sh.] Chapter 5: all; Chapter 7: all.
    Listed reading
  • [E&R] Chapter 6: all.
    Listed reading
  • [Ga.] Chapter 4: all; Chapter 6: all; Chapter 19: Sec. 2.
    Listed reading
  • [Sh.] Chapter 1: 6; Chapter 5: all; Chapter 11: all; Chapter 19: Sec. 2.
    Listed reading
  • [E&R] Chapter 7: all, App. M, N.
    Listed reading
  • [Li.] Chapter 8: Sec. 6; Chapter 9: Sec. 1, 2, and 3; Chapter 10: Sec. 1, 2, and 3.
    Listed reading
  • [Ga.] Chapter 7: all; Chapter 8: Sec. 1, 4, and 5.
    Listed reading
  • [Sh.] Chapter 12: all.
    Listed reading
  • [E&R] Chapter 7: all; App. M, N.
    Listed reading
  • [Li.] Chapter 8: Sec. 2 and 3; Chapter 10: all.
    Listed reading
  • [Ga.] Chapter 4: Sec. c; Chapter 8: all.
    Listed reading
  • [Sh.] Chapter 13: all.
    Listed reading
  • [E&R] Chapter 13: Sec. 1–7.
    Listed reading
  • [Li.] Chapter 8: Sec. 1–4.
    Listed reading
  • [Ga.] Chapter 4: supplements; Chapter 13: all.
    Listed reading
  • SES #: L23 · TOPICS: More on Spin · READING ASSIGNMENTS: <No readings for this session.>
    Reading assignment
  • SES #: L24 · TOPICS: Entanglement: QComputing, EPR, and Bell’s Theorem · READING ASSIGNMENTS: <No readings for this session.>
    Reading assignment

Prerequisites & course information

Prereq: 8.03 and ( 18.03 or 18.032 ) U (Spring) 5-0-7 units. REST Credit cannot also be received for 8.041

Sources