Mastering Quantum Mechanics Part 1: Wave Mechanics (edX)

In this first module of three you will review the basics of wave mechanics and be introduced to the variational principle. You will learn about the technology of spin one-half states and spin operators and get an in-depth look into linear algebra to establish the mathematical foundation necessary to do quantum mechanics. This course concludes by developing the bra-ket notation of Dirac.

To follow this course you will need some basic familiarity with quantum mechanics. You must have seen the Schrödinger equation and studied its solutions for the square well potential, the harmonic oscillator, and the hydrogen atom. You must be proficient in calculus and have some knowledge of linear algebra.

Completing the 3-part Mastering Quantum Mechanics series will give you the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics.
Part 1: Wave Mechanics
Part 2: Quantum Dynamics
Part 3: Entanglement and Angular Momentum

What you'll learn:

- Basics of Wave Mechanics

- Simple Applications of The Variational Principle

- Spin one-half and Spin Operators

- Linear Algebra

- Bra-ket notation

Syllabus

Week 1: Review of wave mechanics. Variational principle.

Week 2: Spin operators and general spin one-half states.

Week 3: Elements of linear algebra: vector spaces and linear operators and matrix representations.

Week 4: Linear algebra: Eigenvalues and eigenvectors, inner product, and adjoint of an operator.

Week 5: Hermitian operators and unitary operators. Dirac bra-ket notation.

Final assessment