Quantum Mechanics I (2020 semester 2)

Prof. Matthew Luzum


Homework



Lectures

Lectures are scheduled for Mondays, Wednesdays, and Thursdays, 2:00-4:00 pm.  Normally, Wednesdays will be used for problem solving sessions.
  • 17 August - Structure of Quantum Mechanics: postulates, Hilbert space (Shankar ch. 1.  Other references: Sakurai ch. 1, Weinberg ch 3, Littlejohn lecture notesJaffe lecture notes)
  • ? 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)
  • ? August - Structure of QM: Normalizable and non-normalizable states, measurement, uncertainty principle (Sakurai Ch. 1, Littlejohn lecture notes)
  • ? 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)
  • ? August - Spatial degrees of freedom -- configuration space wavefunctions, spatial translations, momentum space (LIttlejohn notes)
  • ? August - Time evolution (Littlejohn notes)
  • ? August - Harmonic Oscillator (Littlejohn notes)
  • ? August - Path Integrals (Littlejohn notes)
  • ? September - Path Integrals II  -- stationary phase approximation, classical limit (Littlejohn notes)
  • ? September - Particle in an electromagnetic field, gauge invariance, Aharonov-Bohm effect (Sakurai Ch 2.7)
  • ? September - Rotations/angular momentum (Sakurai Ch 3, Littlejohn classical rotations, Littlejohn spin-1/2 rotations)
  • ? September - Rotations in spin-1/2 systems (Sakurai Ch 3, Littlejohn notes)
  • ? October - Representations, matrix elements, irreducible subspaces (Sakurai Ch 3, LIttlejohn notes)
  • ? October - Orbital angular momentum and spherical harmonics (Sakurai Ch 3, Littlejohn notes)
  • ? October - Central potentials (Littlejohn notes, Sakurai Ch. 3)
  • ? October - Coulomb potential, Hydrogen atom (Sakurai Ch. 3.7 and 4.1)
  • ? October - Addition of angular momenta (Littlejohn notes, Sakurai Ch. 3)
  • ? October - tensor operators, irreducible tensor operators, spherical tensor operators (Sakurai Ch. 3.11, Littlejohn notes)
  • ? October - products of spherical tensor operators, Wigner-Eckart theorem (Sakurai Ch. 3.11, Littlejohn notes)
  • ? November - time-independent perturbation theory; nondegenerate (Sakurai Ch. 5)
  • ? November - degenerate time-independent perturbation theory, variational method (Sakurai Ch. 5)
  • ? November - time-dependent perturbation theory, Dyson series (Littlejohn notes, Sakurai Ch 5)
  • ? November - fine structure of the hydrogen atom (LIttlejohn notes)

Exams

  • Midterm 1 - ? September
  • Midterm 2 - ? November
  • Final Exam - ? November


Suggested textbooks

Main text
  • J.J. Sakurai, "Modern Quantum Mechanics"
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 lowest 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
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HW10.pdf
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HW11.pdf
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HW12.pdf
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HW2.pdf
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HW3.pdf
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HW4.pdf
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HW5.pdf
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HW6.pdf
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HW7.pdf
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HW8.pdf
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HW9.pdf
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Notes.pdf
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