QUANTUM! Seminar
Fall Semester 2000
- Thursday, 31 August: Ensembles and Density Operators
- Thursday, 07 September: Bosons and Fermions
- Thursday, 14 September: Quantum Statistical Mechanics
- Thursday, 21 September: Schroedinger, Heisenberg, and Dirac
Formulations of QM
- Thursday, 28 September: Quantum Dynamics
- Thursday, 05 October: Unitary Representations, Symmetries,
and Group Characters in QM
- Thursday, 12 October: Path Integrals: The Feynman
Formulation of QM
- Thursday, 19 October: Quantum Probability and Quantum Logic
- Thursday, 26 October: Algebraic QM--C* Algebras
- Thursday, 02 November: Quantum Computing, The Basics
- Thursday, 09 November: Quantum Computing, The
Deutsch-Jozsa, Simon, and Grover Algorithms
- Thursday, 16 November: Quantum Computing, Shor's Factoring
Algorithm
- Thursday, 30 November: Quantum Computing, Implementing the
Finite Fourier Transform
- Thursday, 07 December: Quantum Computing, Group Theory and
Quantum Algorithms
QUANTUM! Seminar meets in room 104 LOV at 3:35 on Thursdays. All faculty
and graduate students are welcome. The idea is to give a series of
lectures that develop quantum mechanics in a mathematically honest and
rigorous way. Though we will develop the general theory, after the first
semester we will concentrate on finite-dimensional, or at worst, discrete
spectrum, quantum systems. This frees us from the difficulties that
arise from continuous spectra and gets us quickly into the heart of the
quantum paradoxes and the main goal of my study, quantum computing. A
topics list appears below, admittedly an ambitious program reflecting my
interests. I imagine it will take two years to cover everything.
The topics marked by a double asterisk (**) have already been covered.
QUANTUM! Seminar Topics
- **Historical Survey
- **The Harmonic Oscillator: Classical verses Quantum Treatment
- **Mathematical Structure of Quantum Mechanics (QM)
- **The Dirac Calculus
- **Commutation Relations
- **The Classical Limit: Ehrenfest's Theorem
- **The Quantum Oscillator--Algebraic Treatment
- **Angular Momentum Operators and Spin
- **Multi-Particle States
- **Einstein-Podolsky-Rosen (EPR) Paradoxes and Bell's Inequality
- Ensembles and Density Operators, Traces and Projections
- Bosons and Fermions
- Schroedinger, Heisenberg, and Dirac Formulations of QM
- Quantum Dynamics
- Unitary Representations, Symmetries, and Group Characters in QM
- Path Integrals: The Feynman Formulation of QM
- Quantum Probability and Quantum Logic
- Algebraic QM--C* Algebras
- Quantum Computing
- Shor's Quantum Factoring Algorithm/Grover's Quantum Search Algorithm
- Special Relativity (SR) Primer
- Klein-Gordon and Dirac Equations--Antimatter Predicted!
- Deriving the Hydrogen Spectrum Relativistically
- Deriving the Helium Spectrum through Perturbations
- Quantizing the Classical String
- Quantizing Lagrangian Fields
- Covariant Electrodynamics and its Quantization: Quantum
Electrodynamics (QED)
- Introduction to Quantum Field Theories
Fall Semester 1999
- Thursday, 09 September: Notes on the History of Quantum
Mechanics
- Thursday, 16 September: The Harmonic Oscillator: Classical verses
Quantum Treatment
- Thursday, 23 September: The Quantum Oscillator: Implications of
Quantum Mechanics
- Thursday, 30 September: The Mathematical Structure of Quantum
Mechanics
- Thursday, 07 October: Observables: Self-Adjoint Operators and
Expectation Values
- Thursday, 18 November: The Projection Postulate Examined
- Thursday, 02 December: The Dirac Calculus
Spring Semester 2000
- Thursday, 13 January: The Dirac Calculus: Two Impossible
Equations Habilitated
- Thursday, 20 January: No Seminar--I am in Washington at the AMS
Meeting
- Thursday, 27 January: Commutation Relations
- Thursday, 03 February: Classical Mechanics
Recovered: Ehrenfest's Theorems, Part I: The Equations of Classical
Mechanics
- Thursday, 10 February: Classical Mechanics
Recovered: Ehrenfest's Theorems, Part II: Ehrenfest's Theorems
- Thursday, 17 February: Algebraic Treatment of the Quantum
Oscillator
- Thursday, 24 February: Angular Momentum Operators, Part
I: The
Basics
- Thursday, 02 March: Angular Momentum Operators, Part
II: Representations of su(2)
- Thursday, 16 March: Angular Momentum Operators, Part
III: Application to the Central Force Problem
- Thursday, 23 March: Cancelled for guest lecture
- Thursday, 30 March: Angular Momentum Operators, Part IV:
Spin and Addition Rules
- Thursday, 06 April: Mult-particle States and Tensor
Products
- Thursday, 13 April: Einstein-Podolsky-Rosen (EPR) Paradoxes
and Bell's Inequality
- Thursday, 20 April: EPR and Bell Continued