Quantum Mechanics I

Overview

Contents:
Motivations for studying quantum mechanics - Basic principles of quantum mechanics,Probabilities and probability amplitudes - Linear vector spaces , bra and ket vectors - Completeness, orthonormality, basis vectors - Orthogonal, Hermitian and Unitary operators, change of basis.

Eigenvalues and expectation values, position and momentum representation - Measurement and the generalized uncertainty principle - Schrodinger equation, plane wave solution - Probability density and probability current - Wavepackets and their time evolution - Ehrenfest relations - 1-dimensional potential well problems, particle in a box - Tunnelling through a potential barrier - The linear harmonic oscillator; Operator approach - The linear harmonic oscillator and the Hermite polynomials.

Coherent states and their properties. Application to optics - Other interesting superpositions of basis states such as squeezed light - Motion in 3-dimensions; The central potential problem - Orbital angular momnetum and spherical harmonics - Hydrogen atom ; its energy eigenvalues and eigenfunctions - Additional symmetries of the hydrogen atom - The deuteron ; Estimation of the size of the deuteron - The isotropic oscillator, energy degeneracy - Invariance principles and conservation laws - Spin and the Pauli matrices - Addition of angular momentum - The spin-orbit coupling and its consequences.

Charged particle in a uniform magnetic field; Energy eigenvalues and eigenfunctions - The Schrodinger, and Heisenberg pictures, Heisenberg equations of motion - The interaction picture - The density operator; pure and mixed states, with examples - An introduction to perturbation theory; its relevance, and physical examples - Time-independent perturbation theory : non-degenerate case - Time-independent perturbation theory:degenerate case - Time- dependent perturbation theory; atom- field interactions and the dipole approximation - Examples of time-dependent calculations - Summary of non-classical effects surveyed in the course