Course Details

Subject {L-T-P / C} : PH3005 : Elements of Quantum Mechanics { 3-0-0 / 3}

Subject Nature : Theory

Coordinator : Prof. Sanjoy Datta

Syllabus

Introduction: Young’s double slit and polarized photon experiments – observations, interpretation and necessity of quantum mechanical description. Quantum description of a particle : concept of wave-packet, wave-packet of a free particle and natural emergence of Heisenberg uncertainty relation. Time evolution of a free wave-packet, concept of group velocity and its relation with particle velocity. Time dependent and independent Schrödinger equation: dynamical evolution of a quantum state properties of wave functions, statistical interpretation of wave function, probability current, physical acceptability of wave functions, linearity requirement and superposition principles. Time independent Schrödinger equation and stationary states, energy eigenvalues, completeness of energy eigenfunctions, spread of Gaussian wave-packet for a free particle in one dimension physical interpretation of momentum space wave function and Plancherel theorem. Sturm’s theorem and properties of the zeros of eigenfunctions, qualitative discussion on bound states and scattering states in an arbitrary potential: continuity of wave function, boundary condition and emergence of discrete energy levels. Eigenvalues and eigenfunctions of Hermitian operator. Hamiltonian operator, position, momentum and energy operators commutator of position and momentum operators expectation values of position, momentum and arbitrary quantum mechanical operator. Interpretation of expectation value from experimental point of view. Ehrenfest’s theorem. Applications: One-dimensional problems, energy eigenvalues, eigenfunctions of infinite and finite square well potential Bohr’s correspondence principle delta function potential. Quantum mechanical scattering and tunnelling in one dimension across a step potential & rectangular potential barrier. Simple harmonic oscillator-energy levels and energy eigenfunctions ground state, zero point energy & uncertainty principle, three-dimensional quantum harmonic oscillator and degenerate eigenstates. Hydrogen atom : complete solution of radial and angular equations, wave functions and energy spectrum.

Course Objectives

Course Outcomes

1. A student will have more rigorous and mathematically sound knowledge of quantum mechanical wavefunction. <br />2. A student will learn to solve quantum problems involving time-independent potential. <br />3. Rigorous knowledge about the underlying structure of a quantum problem.

Essential Reading

Supplementary Reading