### Unit: Complex Numbers and Linear Algebra

Note: This Unit does not appear in McIntyre's textbook. However, it is essential that students have a basic familiarity with complex numbers, including Euler's formula, and with linear algebra, including finding eigenvalues and eigenvectors. This Unit represents our approach to that content (7 class hours-10 class hours if you include all of the optional content.)

#### Complex Numbers (20 minutes)

Write these lecture notes, emphasize Euler's formula

#### Introduction to Bra-ket notation (15 minutes)

Ian is turning this into an activity

#### Inner Products and Norms (10 minutes)

• Calculating Inner Products and Normalization of Vectors (Lecture, 10 minutes)

Write these lecture notes. Emphasize complex vectors.

#### Eigenvalues & Eigenvectors (2 hr)

If time allows, cover any or all of the following content. Otherwise, summarize the results and/or work the content into the rest of the Spins course.

### Unit: Background and Stern-Gerlach Experiment

#### Classical Spin

Two approaches are available to introduce the classical spin ideas. One approach, circular loop, is intended for students who had experienced with integral of abstract vectors. The other approach, rectangular loop, is intended for students who only had experienced with explicit vector components. If the time is in essence, quote the result from either approach. Move rectangular loop to homework, write course notes for students and include here for Circular loop from Day 2,3 2016. Comment that adopters who want solutions to any homework can contact us by email. Also solutions to spins hw1, problem 4 e, f.

#### Classical Probabilities (50 minutes)

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 ignored these problems for 15 years and you can safely do so also.

We are working on the following activities intended to address the problems above.

### Unit: Quantum States

#### Review

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

### Unit: Time Dependence

#### Rabi Oscillations & Magnetic Resonance (1 hour 40 minutes)

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