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PAPER II: QUANTUM MECHANICS

Unit I
: Equation of Motion & Application of Schroedinger’s Equation State Vectors-Hilbert Space-Dirac Notation-Dynamical Variables as Operators-Change of Basis-

Unitary Transformation-Equation of Motion in Schroedinger Picture, Heisenberg Picture & Dirac Picture-Representation of Operators by Matrices-One Dimensional Linear Harmonic Oscillator in Matrix Mechanics.-Kronig Penny Model

Unit II
: Approximate Methods Time Independent Perturbation Theory in Non-Degenerate Case-Ground State of Helium Atom-Degenerate Case-Stark Effect in Hydrogen-Variation Method & its Application to Hydrogen Molecule-WKB Approximation. Time Dependent Perturbation Theory: Time Dependent Perturbation Theory-First and Second Order Transitions-Transition to Continuum of States-Fermi Golden Rule-Constant and Harmonic Perturbation-Transition Probabilities-Selection Rules for Dipole Radiation-Collision-Adiabatic Approximation

Unit III
: Angular Momentum Orbital Angular Momentum-Spin Angular Momentum-Total Angular Momentum Operators-Commutation Relations of Total Angular Momentum with Components-Ladder Operators-Commutation Relation of Jz with J+ and J- - Eigen Values of J2, Jz -Matrix Representation of J2, Jz, J+ and J- - Addition of Angular Momenta- Clebsch Gordon Coefficients- Properties. Relativistic Wave Equation: Klein Gordon Equation-Plane Wave Equation-Charge and Current Density-Application to the Study of Hydrogen Like Atom-Dirac Relativistic Equation for a Free Particle-Dirac Matrices-Dirac Equation in Electromagnetic Field-Negative Energy States-Dirac’s Equation in a Central Field(Electron Spin)-Spin Orbit Energy.

Unit IV
: Scattering Theory Scattering Amplitude-Expression in terms of Green’s Function-Born Approximation and its Validity-Partial Wave Analysis-Phase Shifts-Scattering by Coulomb and Yukawa Potential Application to Atomic Structure Central Field Approximation-Thomas Fermi Model-Hartree’s Self Consistent Model- Hartree Fock Equation-Alkali Atoms-Doublet Separation-Intensities-Complex Atoms-Coupling Schemes Application to Molecular Structure Hydrogen Molecule Ion-Hydrogen Molecule-Heitler London Method-Covalent Bond- Spin Orbit Interaction as Correction to Central Field Approximation- Hartree Fock Self Consistent Field Method for Molecules-Hybridisation.

Unit V
: Theory of Radiation (Semi Classical Treatment) Einstein’s Coefficients-Spontaneous and Induced Emission of Radiation from Semi Classical Theory-Radiation Field as an Assembly of Oscillators-Interaction with Atoms- Emission and Absorption Rates-Density Matrix and its Applications Quantum Field Theory Quantization of Wave Fields- Classical Lagrangian Equation-Classical Hamiltonian Equation-Field Quantization of the Non-Relativistic Schroedinger Equation-Creation, Destruction and Number Operators-Anti Commutation Relations-Quantization of Electromagnetic Field Energy and Momentum.

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