Course Overview

FIXME: Course Site Under Construction.

The “Quantum Measurements and Spin” course is built upon the quantum mechanical two state system. The first of the Quantum Paradigms, this course introduces students to quantum mechanics by beginning with the postulates of quantum mechanics and how the postulates are used to gather information about quantum mechanical systems. The common spin-up and spin-down state vectors with x,y, and z-orientation will be derived, and the general state vector $\vert \psi (\theta,\phi ) \rangle$ will also be introduced. Throughout the class, students perform several simulated experiments with virtual Stern-Gerlach devices and interpret their results (Spins OSP software). Operators that correspond to physical observables in quantum experimentation are then presented; students will learn in particular about spin operators, projection operators, the density operator, and the Hamiltonian. Important physical relations among these quantum operators will also be made using the commutators, uncertainty relations, and expectation values. Spin 1 systems are also introduced as an additional context for exploring and interpreting Stern-Gerlach experiments. The time evolution of quantum states using the Schrodinger Equation will also be explored to investigate time dependence in probabilities, uncertainties, and expectation values. The course ends with introductions to special topics of spin precession, Rabi oscillations, and magnetic resonance. (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

Activities Included

Unit: Introduction

Classical Probabilities (50 minutes)

FIXME This topic was originally part of Spins Lab 1. There are two problems with that lab. First, that students don't understand the mean as a weighted average. Second, that the effect of binning data is not clear. We are currently working on activities that address these problems. In the meantime, we ignored them for 15 years and you can safely do so also.

Classical Spin (1 hr or a bit more)

The Stern-Gerlach Experiment (30 minutes)

Unit: Quantum States

Quantum State Vectors, Probability (45 minutes)


You may need to sprinkle these review topics several times each throughout the course!

Finding Expressions for Unknown Quantum States (2 hours 15 minutes)

Unit: Quantum Operators

Projection (60 minutes)

Measurement (2 hours 25 minutes)

Commutators & Uncertainty Relations (1 hour 10 minutes)

Density Operator (Optional - Advanced, 50 minutes)

Unit: Topics in Quantum Mechanics

Time Evolution (2 hours 30 minutes)

Rabi Oscillations & Magnetic Resonance (1 hour 40 minutes)

Unit: Quantum Spookiness

Optional topics - can be skipped (In 2008-2010 we had a gues lecturer speak on one of the following topics. Their lecture notes or powerpoint slides are included as a resource.)

Quantum Clocks

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)
  • Appropriate homework problems are at the end of Chapter 4

Quantum Cryptography

Spins SWBQs

FIXME - In process of editing. See Master SWBQ List at “Pedagogy” → “Small Whiteboard Questions”

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