Quantum Mechanics I (2017 semester 2)

Prof. Matthew Luzum
Sala 202, Ala II

Monitor:  Daniel Teixeira
Sala 329, Ala Central


Homework



Lectures

Lectures are scheduled for Mondays, Wednesdays, and Thursdays, 2:00-4:00 pm.
  • 7 August - Structure of Quantum Mechanics: postulates, Hilbert space (Shankar ch. 1.  Other references: Sakurai ch. 1, Weinberg ch 3, Littlejohn lecture notesJaffe lecture notes)
  • 10 August - Structure of QM: Operators; commutators, outer product, resolutions of the identity, Hermitian anti-Hermitian and Unitary operators, spectra (Shankar Ch. 1, Littlejohn lecture notes)
  • 14 August - Structure of QM: Normalizable and non-normalizable states, measurement, uncertainty principle (Sakurai Ch. 1, Littlejohn lecture notes)
  • 17 August - Application of postulates to a physical system -- Stern-Gerlach experiment; Mixed states and the density operator (Littlejohn Stern-Gerlach , Littlejohn density operator, Sakurai Ch. 1)
  • 23 August - Spatial degrees of freedom -- configuration space wavefunctions, spatial translations, momentum space (LIttlejohn notes)
  • 24 August - Time evolution (Littlejohn notes)
  • 28 August - Harmonic Oscillator (Littlejohn notes)
  • 31 August - Path Integrals (Littlejohn notes)
  • 11 September - Path Integrals II  -- stationary phase approximation, classical limit (Littlejohn notes)
  • 14 September - Particle in an electromagnetic field, gauge invariance, Aharonov-Bohm effect (Sakurai Ch 2.7)
  • 25 September - Rotations/angular momentum (Sakurai Ch 3, Littlejohn classical rotations, Littlejohn spin-1/2 rotations)
  • 28 September - Rotations in spin-1/2 systems (Sakurai Ch 3, Littlejohn notes)
  • 2 October - Representations, matrix elements, irreducible subspaces (Sakurai Ch 3, LIttlejohn notes)
  • 5 October - Orbital angular momentum and spherical harmonics (Sakurai Ch 3, Littlejohn notes)
  • 9 October - Central potentials (Littlejohn notes, Sakurai Ch. 3)
  • 16 October - Coulomb potential, Hydrogen atom (Sakurai Ch. 3.7 and 4.1)
  • 18 October - Addition of angular momenta (Littlejohn notes, Sakurai Ch. 3)
  • 23 October - Irreducible tensor operators, Wigner-Eckart theorem

Exams

  • Midterm 1 - 21 September
  • Midterm 2 - 1 November (estimated)
  • Final Exam - 20 November (estimated)


Suggested textbooks

Main text
  • J.J. Sakurai, "Modern Quantum Mechanics", (chapter numbers refer to Revised Edition, not Second Edition)
Other texts
  • Shankar, Principles of Quantum Mechanics.
  • Weinberg, Lectures on Quantum Mechanics


Evaluation

Grades will be based on homework (10%) and the best 2 out of 3 exams (45% each).  

The two midterm exams will cover ~50% of the material, and the final exam will review the entire semester. The worst score of the three exams will be dropped, and the remaining 2 scores will determine 90% of your final grade.


Program

Tentative list of topics:
  • General structure of quantum mechanics
  • Examples
  • Angular momentum / spin
  • Approximation methods


Lecture Notes


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HW1.pdf
(106k)
Matt Luzum,
Jul 19, 2017, 9:08 AM
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Matt Luzum,
Aug 14, 2017, 9:32 AM
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HW2.pdf
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Matt Luzum,
Aug 13, 2017, 3:27 PM
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Matt Luzum,
Aug 21, 2017, 10:02 AM
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HW3.pdf
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Matt Luzum,
Aug 19, 2017, 2:14 PM
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Matt Luzum,
Aug 28, 2017, 9:53 AM
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HW4.pdf
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Matt Luzum,
Aug 27, 2017, 10:29 AM
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Matt Luzum,
Sep 11, 2017, 7:19 AM
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HW5.pdf
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Matt Luzum,
Sep 4, 2017, 12:54 PM
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Matt Luzum,
Sep 18, 2017, 10:02 AM
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HW6.pdf
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Matt Luzum,
Sep 28, 2017, 7:07 AM
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Matt Luzum,
Oct 3, 2017, 12:13 PM
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HW7.pdf
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Matt Luzum,
Oct 9, 2017, 4:07 AM
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Matt Luzum,
Oct 9, 2017, 4:07 AM
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HW8.pdf
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Matt Luzum,
Oct 9, 2017, 4:07 AM
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Matt Luzum,
Oct 16, 2017, 12:06 PM
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HW9.pdf
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Matt Luzum,
Oct 16, 2017, 7:32 AM
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Notes.pdf
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Matt Luzum,
Oct 16, 2017, 7:32 AM