This course on Quantum Mechanics covers a wide range of topics in Quantum Physics. By the end of the course, learners will understand key concepts of Quantum Mechanics, probability distributions, wave functions, uncertainty principles, Schrodinger equations, stationary states, quantum harmonic oscillators, free particles, linear algebra in Quantum Mechanics, angular momentum, spin, and energy levels in solids. The course employs a lecture-based teaching method and is suitable for individuals interested in delving into the foundational principles of Quantum Physics.
Overview
Syllabus
) Introduction to quantum mechanics.
) The domain of quantum mechanics.
) Key concepts of quantum mechanics.
) A review of complex numbers for QM.
) Examples of complex numbers.
) Probability in quantum mechanics.
) Variance of probability distribution.
) Normalization of wave function.
) Position, velocity and momentum from the wave function.
) Introduction to the uncertainty principle.
) Key concepts of QM - revisited.
) Separation of variables and Schrodinger equation.
) Stationary solutions to the Schrodinger equation.
) Superposition of stationary states.
) Potential function in the Schrodinger equation.
) Infinite square well (particle in a box).
) Infinite square well states, orthogonality - Fourier series.
) Infinite square well example - computation and simulation.
) Quantum harmonic oscillators via ladder operators.
) Quantum harmonic oscillators via power series.
) Free particles and Schrodinger equation.
) Free particles wave packets and stationary states.
) Free particle wave packet example.
) The Dirac delta function.
) Boundary conditions in the time independent Schrodinger equation.
) The bound state solution to the delta function potential TISE.
) Scattering delta function potential.
) Finite square well scattering states.
) Linear algebra introduction for quantum mechanics.
) Linear transformation.
) Mathematical formalism is Quantum mechanics.
) Hermitian operator eigen-stuff.
) Statistics in formalized quantum mechanics.
) Generalized uncertainty principle.
) Energy time uncertainty.
) Schrodinger equation in 3d.
) Hydrogen spectrum.
) Angular momentum operator algebra.
) Angular momentum eigen function.
) Spin in quantum mechanics.
) Two particles system.
) Free electrons in conductors.
) Band structure of energy levels in solids.
Taught by
Academic Lesson
