1. Linear Algebra in Quantum Mechanics#

This chapter summarises concepts that you are familiar with from your linear algebra and quantum mechanics courses and that are the most relevant to computational chemistry. It is meant as a review rather than an introduction. The first paragraphs deal with the fundamental concepts, and practical examples in quantum mechanics shall be given towards the end of the chapter along with a set of exercises. (For those interested, some additional information is given in parentheses; you may find this useful if you ever wish to go through the literature.)

🎯 Learning goals

Review basic concept of linear algebra

Review basic notation of quantum mechanics

Basic vector operations using Numpy

📖 Chapter in script

Chapter 2 - Basic principles of Quantum Mechanics

Appendix A.1 - Vector space and scalar product

📚 Resources

Cohen-Tannoudji, C., Diu, B., & Laloe, F. (1986). Quantum Mechanics, Volume 1.

  • Chapter II B - State space, Dirac notation

  • Chapter II C - Representations in the state space

  • Chapter II D - Eigenvalue equations, observables

  • Chapter II E - Two important examples of represantations and observables

  • Chapter II Complement \(\text{D}_{\text{II}}\) - A more detailed study of the \(\{|r\rangle\}\) and \(\{|p\rangle\}\) representations

  • Chapter II Complement \(\text{E}_{\text{II}}\) - Some general properties of two observables, \(Q\) and \(P\), whose commutator is equal to \(i\hbar\)