Quantum Measurement and Spin

This course is centered around the quantum mechanical two state system. This course is the first of the quantum paradigms and introduces students to quantum mechanics by leading off with the postulates of quantum mechanics. A central theme of this course is having students perform some simulated experiments with Stern-Gerlach devices and interpret their results. Students learn about quantum measurement, Dirac Notation, vector spaces, quantum mechanical operators, commuting observables, incompatible observables, the uncertainty principle, and time-evolution of quantum states. Spin 1 systems are also introduced as a second context for exploring and interpreting Stern-Gerlach experiments. The course ends with introductions to special topics like Rabi oscillations, neutrino oscillations, magnetic resonance, the EPR paradox, and quantum computing. (more...)

Textbook: Quantum Mechanics: A Paradigms Approach—-a textbook that follows the paradigms approach. The chapters that are relevant to the Quantum Measurement and Spins course are: the appendix on linear algebra: Linear Algebra and Matrices, Chapter 1: Stern-Gerlach Experiments, Chapter 2: Operators and Measurement, Chapter 3: Schrödinger Time Evolution and Chapter 4: Quantum Spookiness, and the Instructor's Guide

Sample Syllabus: 425_syllabus_wi10.doc

Course Contents

Unit: Stern-Gerlach Experiments

Historic Stern-Gerlach Experiment (70 minutes)

Probability and Statistics (30 minutes)

Using Stern-Gerlach Observations to Build Quantum State Formalism (245 minutes)

Generalized Spin Systems (20 minutes)

Unit: Operators and Measurement

Operators, Eigenvalues, and Eigenvectors

Expectation Value, Standard Deviation, Commutation, and Uncertainty

Spin-1 Systems

The $S$ and $S^2$ Vectors (XX minutes)

Unit: Schrödinger Time Evolution

Schrodinger equation, energy eigenvalues and eigenstates

Spin Precession

Neutrino Oscillation

Optional topic - can be skipped

Magnetic Resonance

Optional topic - can be skipped

  • Here are slides that can be used for this topic (Lecture, 40 minutes): nmr.pdf
  • Appropriate homework problems can be chosen from the end of Chapter 3, none explicitly address this topic

Unit: Quantum Spookiness

Optional topics - can be skipped

(What we have done from 2008-2010 is have a guest lecturer speak on one of the following topics)

Quantum Clocks

  • Here is a scan of the lecture notes from the invited guest lecturer (Lecture, 60 minutes): 425_guest_lecture.pdf
  • There have not been homework problems designed for this guest lecture

EPR Paradox

  • Here are slides addressing this topic (Lecture, 60 minutes): bells_inequality.pdf
  • Additional reading of interest: a paper giving an Sherlock Holmes-type analogy to Bell's theorem bells_theorem.pdf
  • Appropriate homework problems are at the end of Chapter 4

Schrodinger Cat Paradox

  • There are no current lecture notes for this topic, addressed in chapter 4 (Lecture, 60 minutes)
  • Here are slides for the related topic of Quantum Cryptography: quantum_cryptography.pdf
  • Appropriate homework problems are at the end of Chapter 4

Activities Included

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