# What's a good book on supersymmetric quantum mechanics for an undergraduate?

I'm a third-year undergraduate student, and halfway through a seminar on quantum mechanics, my second course in the subject. This semester, we've used Townsend's A Modern Approach to Quantum Mechanics, second edition, and covered

• Stern-Gerlach experiments
• Some matrix mechanics
• Angular momentum, as well as adding spin
• Time evolution and the Schrödinger equation
• Wave mechanics
• The one-dimensional harmonic oscillator
• A brief, but (the professor says) somewhat rigorous introduction to path integrals

A couple weeks ago, I presented a problem that used a basic superpotential to analyze the 1D harmonic oscillator, using the operator $$\hat{A}=W(\hat{x})+\frac{i}{\sqrt{2m}}\hat{p}_x$$ and from there finding $$\hat{A}^{\dagger}$$, $$W$$, etc.

I'm interested in learning more about supersymmetric quantum mechanics, so I'm looking for a textbook that would be suitable for an undergraduate like myself. As I don't know much about superpotentials and related tools, I'm having a hard time asking about specific subtopics I'd want it to cover - certainly superpotentials, as well as superalgebras. Having exercises and examples is a must for me.

I'm hoping for some mathematical rigor, too. I feel quite solid when it comes to linear algebra and calculus, as well as introductory group theory (including Lie groups, Lie algebras, etc.) and real analysis. I'm willing to wait until the end of the course before doing more reading in this area; later in the semester, we'll discuss central potentials, time-independent perturbations, scattering (in more detail than we've covered to date), and problems with identical particles. We'll follow the textbook fairly closely.

Are there any textbooks on supersymmetric quantum mechanics that would suit me, given my current level of knowledge of quantum mechanics and mathematics?

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• Maybe chapter 10 (and 9) of the book Mirror Symmetry is a good place to start. (Available for free at the link) – Elliot Schneider Mar 14 at 16:07