Week 1
- Black-body radiation and its spectral energy density; black body as a cavity, energy density inside a cavity, radiation pressure
- Stefan-Boltzmann law, Wien’s displacement law, Wien’s formula for spectral density
- Relation between energy density and average oscillator energy, quantum hypothesis for oscillators and resulting spectral density
- More on quantizitaion concept – specific heat of insulators; photoelectric effect
- Spectrum of hydrogen atom and Bohr model
- Wilson-Sommerfeld quantization condition and application to particle in a box and harmonic oscillator
Week 2
- Application of Wilson-Sommerfeld quantization conditions to atoms-I
- Application of Wilson-Sommerfeld quantization conditions to atoms-II and quantum numbers
- Periodic Table and electron spin
- Interaction of light with matter- Einstein’s A and B coefficients
- Life-time of an excited-state, LASERS
- Towards quantum-mechanics: The correspondence principle
Week 3
- The correspondence principle and selection rules
- Heisenberg’s formulation of quantum-mechanics I: The variables as matrix elements I
- Heisenberg’s formulation of quantum-mechanics II: The quantum condition
- Heisenberg’s formulation of quantum-mechanics III: Solution for harmonic oscillator
- Matrix mechanics – general discussion
- Matrix mechanics – general discussion
Week 4
- Introduction to waves and wave equation
- Stationary waves and eigenvalues; time-dependence of a general displecement
- de Broglie waves and their experimental verification
- Representation of a particle as a wavepacket
- Time-independent Schrödinger equation; properties of its solutions. Solution for
- Solution of Schrodinger equation for particle in a harmonic potential
Week 5
- Equivalence of Heisenberg and Schrödinger formulation-I
- Equivalence of Heisenberg and Schrödinger formulation-II
- Born-interpretation of wavefunction and expectation values
- The uncertainty principle and simple applications
- Time-depepndent Schrödinger equation and current density
- Comparison with Newton’s equations: Ehrenfest’s theorems
Week 6
- Examples of solution of one-dimensional Schrödinger equation – Particle in one and two delta function potentials
- Solution of one-dimensional Schrödinger equation for particle in a finite well
- Numerical solution of one-dimensional Schrödinger equation for bound-states-I
- Numerical solution of one-dimensional Schrödinger equation for bound-states-II
- Reflection and transmission of particles across a potential barrier
- Quantum-tunneling and its examples
Week 7
- Solution of Schrödinger equation for free particles and periodic boundary conditions
- Electrons in a metal: Density of states, Fermi energy
- Schrödinger equation for particles in spherically symmetric potentials, angular momentum operator
- Angular momentum operator and its eigenfucntions
- Equation for the radial component of wavefunction for spherically symmetric potentials and general properties of its solution
- Solution for the radial component of wavefunction for the hydrogen atom
Week 8
- Numerical solution for the radial component of wavefunction for spherically symmetric potentials
- Solution of Schrodinger equation for one-dimensional periodic potential: Bloch’s theorem
- Kroning-Penny model and energy bands
- Kroning-Penny model and energy bands
- Numerical calculation of bands
- REVIEW