pdusu exam paper 2016
Eigenvalues and eigenfunctions; expectation values of operators: position, momentum, energy: Ehrenfest theorem and complementarity, Concept of group and phase velocity, wave packet, Gaussian wave packet, bra-ket notation.Unit - II : Schrödinger wave cquation and its solutions
1. Schrödinger wvave equation: general equation of wave propagation, propagation of time dependent and time-independent Schrödinger equation,natter saves, uavefunction representation (v). physical meaning of y. properties and conditions on v, postulates of wave mechanics, operators, observable and measurements; probability current density.2. Time independent Schrödinger equation, staționary state solution, one dimensional oblemt: particle in one dimensional box, eigenfunctions and eigenvalues, discrete EKIkvels, gencralization into. three dimension and degeneracy of energy levels, concept of a potential well and barrier, stęp potential, penetration through rectangular barrier, reflection and transmission coefficients, barriers with special shapes (graphical representation), quantum mechanical tunneling (alpha decay).
Unit - III : Schrodinger equation solutions in special cases
1. Symmetric square well potential, reflection and vansmission coefticients, resonant scattering, Bound state problems: particle in one dimensional infinite potential well and finite depth potential well, energy eigenvalues and eigenfunctions, transcendental equation and its solution; Simple harmonic oscillater. Schrödinger equation for simple harmonic oscillator and its soluzion, eigenfunction, eigenvalues, zero point energy, quantum and classical probability density, parity. symmetric and antisymmetric wave lunctions with graphical representation.2. Schrödinger cquation in spherical coordinates, Schrödinger equation for one eldueerom in spherical coordinates, separation into radial and angular variables, soluionradial equation and angular equation, qualitative discussion of spherical harmonics, series solution and encrgy cigenvalues, stationary state wavefunction. Wave-functions of H-atom for ground and tirst excited states, average radius of H-atom, Bohr correspondence principle, orbital angular momentum and its quantization, commutation relation, eigenvalues and eigenfunctions,