PHY3101 QUANTUM MECHANICS II

This is a second course in undergraduate quantum mechanics which prepares students for advanced studies in quantum physics. It treats various approximation methods for stationary states and time dependent perturbation theory. The course treats both angular momentum and spin leading to addition of angular momenta. The eigenvalues and eigen functions of the Hamiltonian for the Hydrogen atom are considered including the splitting of energy levels by application of a magnetic field. The laser and maser principles are introduced

Course Objectives
At the end of the course, the students should be able to

• Show how quantum states evolve in time
• Apply the variational method to estimate the ground state energy and wave function for a given Hamiltonian
• Apply the time independent perturbation theory to estimate eigenvalues and eigenstates of a given Hamiltonian. 
• Apply the time dependent perturbation theory to determine approximate eigenstates and eigenvalues of simple time dependent Hamiltonians
• Use the Born Approximation to calculate approximate values of differential scattering cross-sections for given scattering potentials
• Apply partial wave analysis to calculate cross-sections for scattering at low energies
• Derive the commutation relations involving the Cartesian components of the angular momentum and find the eigenvalues of  
• Use a method of separation of variables to solve Schrödinger equation for the Hydrogen atom and explain the significance of the quantum numbers  

Expected Learning outcomes
At the end of the course the students should be able to

• Estimate the ground state energy and wave function for a given Hamiltonian using variational method
• Estimate eigenvalues and eigenstates of a given Hamiltonian using time independent perturbation theory
• Determine approximate eigenstates and eigenvalues of simple time dependent Hamiltonians using time dependent perturbation theory
• Calculate approximate values of differential scattering cross-sections for given scattering potentials using Born’s approximation and partial wave analysis
• Calculate the cross-sections for scattering at low energies
• Solve Schrödinger equation for the Hydrogen atom and explain the significance of the quantum numbers