Chapter 1

Time Dependent Schrodinger Equation

Time dependent wave equation

medium • 1 min read

Physical interpretation of wave function

medium • 2 min read

Probability current density

medium • 3 min read

Normalization of wave function

medium • 4 min read

Conservation of probability

medium • 5 min read

Chapter 2

Time Independent Schrodinger Equation

Separation of variables

medium • 1 min read

Stationary states

medium • 2 min read

Properties of eigen functions

medium • 3 min read

Boundary conditions

medium • 4 min read

Degeneracy

medium • 5 min read

Chapter 3

Operators and Expectation Values

Momentum and energy operators

medium • 1 min read

Hermitian operators

medium • 2 min read

Commutator relations

medium • 3 min read

Expectation values

medium • 4 min read

Ehrenfest's theorem

medium • 5 min read

Chapter 4

One Dimensional Potentials

Particle in a 1D rigid box

medium • 1 min read

Finite potential well

medium • 2 min read

Potential step and reflection

medium • 3 min read

Quantum tunneling through a barrier

medium • 4 min read

Linear harmonic oscillator (algebraic)

medium • 5 min read

Chapter 5

Quantum Theory of Hydrogen Atom

Schrodinger equation in spherical coordinates

medium • 1 min read

Separation into radial and angular parts

medium • 2 min read

Quantum numbers (n, l, m)

medium • 3 min read

Radial probability distribution

medium • 4 min read

Energy levels of Hydrogen

medium • 5 min read

Chapter 6

Angular Momentum and Spin

Orbital angular momentum operators

medium • 1 min read

Commutation relations of angular momentum

medium • 2 min read

Eigenvalues of L^2 and L_z

medium • 3 min read

Electron spin hypothesis

medium • 4 min read

Pauli spin matrices

medium • 5 min read