Mathematical Tools of Quantum Mechanics
In this chapter we will dicuss and visulise following topics:
- One particle wave function space
- State space, Dirac notation
- Projection operator, Hermitian conjugation
- Representation in state space
- Eigenvalue equations, observables
- Complete sets of commuting observables
Postulates of Quantum Mechanics
In this chapter we will dicuss and visulise following topics:
- Statement of the postulates
- Physical interpretation
- Physical implications of the Schrodinger equation: superposition principle
- Conservation of probability
- Equation of motion for an observable, principle of first quantization
- Ehrenfest theorem
Barriers and Bound States in One Dimension
In this chapter we will dicuss and visulise following topics:
- Particle in a box and Box normalization
- Concept of potential: potential with finite walls, step and barrier
- Free particle in an infinite and finite potential well
- Reflection and transmission coefficient
- Interpretation tunneling effect
- Ramsauer Townsend effect
- Smooth barrier
- Cold emission of electrons in a metal: scanning tunneling microscope
- Alpha decay: Geiger Nuttal law
- Virtual binding
- Double well model of a molecule
- Kronig-Penny model for metals
- Revision of angular momentum in spherical coordinates
Spin and Magnetic Moment
In this chapter we will dicuss and visulise following topics:
- Need for matrix representation of spin
- Pauli spin matrices
- Spinors and expectation values
- Pauli operators
- Magnetic moment of an electron
- Precession of an electron in a magnetic field, magnetic resonance
- Space inversion
- Time reversal
- Isospin
Addition of Angular Momenta
In this chapter we will dicuss and visulise following topics:
- Addition of two spins
- Addition of two angular momenta: general method
- Vector operators: Wigner-Eckart theorem
- Identical particles and symmetry
Stationary Perturbation theory
In this chapter we will dicuss and visulise following topics:
- Perturbation theory
- Nondegenerate case and Simple applications
- Degenerate case, Simple cases of removal of degeneracy
- Exchange degeneracy
- Rayleigh Ritz Variation Method