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Advanced Quantum Mechanics: Course Outline (PH-604)

Quantum mechanics including quantum field theory, is a fundamental branch of physics concerned with processes involving, for example,atoms and photons

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Course Outline

Introduction to quantum mechanics, quantum theory and the wave nature of matter, the wave function and its interpretation, Wave packets and free particle motion, superposition principle, wave packet and uncertainty relation, Motion of a wave packet, The wave equation, The wave function and the Schrödinger equation, justification of the wave equation, the interpretation of and the conservation of probability, expectation values of dynamic variables and operators stationary state solutions, general solution of the wave equation, The linear harmonic oscillator, Eigen values and Eigen functions, the double oscillator, the double oscillator Eigen values and Eigen functions, The WKB approximation, the connection formulas, transmission through barrier, The principle of wave mechanics, coordinates and momentum representations, Hermitian operators, their Eigen values and Eigen functions, superposition of Eigen states, simultaneous measurements and computing operators, Central forces and angular momentum, orbital angular momentum, kinetic energy and angular momentum, the Eigen values problem for L2 and Lz,The intrinsic angular momentum, spin as a dynamic variable, spin and rotations, spin and reflections, Perturbation theory, non-degenerate perturbation theory, degenerate perturbation theory, application to atoms, Variable methods, helium atom, time dependent perturbation theory, Coulomb excitation, the atom in a radiation field, Scattering, the scattering of a wave packet, Green function in scattering theory, The Born approximation, phaseshifts, scattering resonances, phase shifts and green s functions, Coulombs scattering integral equations of scattering theory, properties of scattering states, the scattering matrix, The Schrodinger Equation in First and Second Quantization, Fermi Systems, Linear Response and Collective Modes, Bose Systems, Weakly Interacting Bose Gas, Field Theory At finite Temperature ,physical systems at finite temperature real-time green’s functions and linear response, Canonical transformations, Nuclear Matter Phonons and Electrons, superconductivity.

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