Here’ is a great (and free) course covering quantum mechanics.

Quantum physics also known as Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all #quantum #physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.

Table of Contents:

- (0:00:00) Introduction to quantum mechanics
- (0:16:23) The domain of quantum mechanics
- (0:24:18) Key concepts of quantum mechanics
- (0:34:04) A review of complex numbers for QM
- (0:48:12) Examples of complex numbers
- (1:01:47) Probability in quantum mechanics
- (1:12:17) Variance of probability distribution
- (1:26:16) Normalization of wave function
- (1:51:47) Position, velocity and momentum from the wave function
- (2:10:59) Introduction to the uncertainty principle
- (2:24:32) Key concepts of QM – revisited
- (2:37:45) Separation of variables and Schrodinger equation
- (3:09:55) Stationary solutions to the Schrodinger equation
- (3:15:47) Superposition of stationary states
- (3:25:37) Potential function in the Schrodinger equation
- (3:48:10) Infinite square well (particle in a box)
- (4:00:58) Infinite square well states, orthogonality – Fourier series
- (4:08:07) Infinite square well example – computation and simulation
- (4:39:27) Quantum harmonic oscillators via ladder operators
- (5:16:48) Quantum harmonic oscillators via power series
- (5:28:32) Free particles and Schrodinger equation
- (5:34:37) Free particles wave packets and stationary states
- (6:10:33) Free particle wave packet example
- (6:13:43) The Dirac delta function
- (6:20:49) Boundary conditions in the time independent Schrodinger equation
- (6:24:39) The bound state solution to the delta function potential TISE
- (6:43:29) Scattering delta function potential
- (6:55:49) Finite square well scattering states
- (7:07:39) Linear algebra introduction for quantum mechanics
- (7:10:34) Linear transformation
- (7:13:04) Mathematical formalism is Quantum mechanics
- (7:37:52) Hermitian operator eigen-stuff
- (8:01:23) Statistics in formalized quantum mechanics
- (8:24:26) Generalized uncertainty principle
- (8:54:36) Energy time uncertainty
- (9:16:33) Schrodinger equation in 3d
- (9:19:56) Hydrogen spectrum
- (9:31:14) Angular momentum operator algebra
- (9:57:17) Angular momentum eigen function
- (10:18:08) Spin in quantum mechanics
- (10:22:23) Two particles system
- (10:58:03) Free electrons in conductors
- (11:09:23) Band structure of energy levels in solids