Advanced Quantum Mechanics-Theory(M.Sc)
PHYSICXION: notes of wkb, time dependent perturbation, scattering, symmetry and relativistic quantum mechanics
What you will find in this module are as follows: Only Theory in brief and to the point
WKB Approximation
Quantization rule, tunneling through a barrier, qualitative discussion of α-decay.
Time-dependent Perturbation Theory
Time-dependent perturbation theory, interaction picture; Constant and harmonic perturbations — Fermi’s Golden rule; Sudden and adiabatic approximations.
Scattering theory
Laboratory and center of mass frames, differential and total scattering cross-sections, scattering amplitude; Scattering by spherically symmetric potentials; Partial wave analysis and phase shifts; Ramsauer-Townsend effect; Relation between sign of phase shift and attractive or repulsive nature of the potential; Scattering by a rigid sphere and square well; Coulomb scattering; Formal theory of scattering — Green’s function in scattering theory; Lippman-Schwinger equation; Born approximation.
Symmetries in quantum mechanics
Conservation laws and degeneracy associated with symmetries; Continuous symmetries — space and time translations, rotations; Rotation group, homomorphism between SO(3) and SU(2); Explicit matrix representation of generators for j = 1/2 and j = 1; Rotation matrices; Irreducible spherical tensor operators, Wigner-Eckart theorem; Discrete symmetries — parity and time reversal.Identical Particles
Meaning of identity and consequences; Symmetric and antisymmetric wavefunctions; Slater determinant; Symmetric and antisymmetric spin wavefunctions of two identical particles; Collisions of identical particles.
Relativistic Quantum Mechanics
Klein-Gordon equation, Feynman-St¨uckelberg interpretation of negative energy states and concept of antiparticles; Dirac equation, covariant form, adjoint equation; Plane wave solution and momentum space spinors; Spin and magnetic moment of the electron; Nonrelativistic reduction; Helicity and chirality; Properties of γ matrices; Charge conjugation; Normalisation and completeness of spinors.
Quantization rule, tunneling through a barrier, qualitative discussion of α-decay.
Time-dependent Perturbation Theory
Time-dependent perturbation theory, interaction picture; Constant and harmonic perturbations — Fermi’s Golden rule; Sudden and adiabatic approximations.
Scattering theory
Laboratory and center of mass frames, differential and total scattering cross-sections, scattering amplitude; Scattering by spherically symmetric potentials; Partial wave analysis and phase shifts; Ramsauer-Townsend effect; Relation between sign of phase shift and attractive or repulsive nature of the potential; Scattering by a rigid sphere and square well; Coulomb scattering; Formal theory of scattering — Green’s function in scattering theory; Lippman-Schwinger equation; Born approximation.
Symmetries in quantum mechanics
Conservation laws and degeneracy associated with symmetries; Continuous symmetries — space and time translations, rotations; Rotation group, homomorphism between SO(3) and SU(2); Explicit matrix representation of generators for j = 1/2 and j = 1; Rotation matrices; Irreducible spherical tensor operators, Wigner-Eckart theorem; Discrete symmetries — parity and time reversal.Identical Particles
Meaning of identity and consequences; Symmetric and antisymmetric wavefunctions; Slater determinant; Symmetric and antisymmetric spin wavefunctions of two identical particles; Collisions of identical particles.
Relativistic Quantum Mechanics
Klein-Gordon equation, Feynman-St¨uckelberg interpretation of negative energy states and concept of antiparticles; Dirac equation, covariant form, adjoint equation; Plane wave solution and momentum space spinors; Spin and magnetic moment of the electron; Nonrelativistic reduction; Helicity and chirality; Properties of γ matrices; Charge conjugation; Normalisation and completeness of spinors.
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Chp-1: WKB-Approximation  |
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Chp-2: Time-Dependent Perturbation  |
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Chp-3: Scattering Theory |
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Chp-4: Symmetries in Quantum Mechanics(COMING SOON) |
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Chp-5: Identical Particles(COMING SOON)  |
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Chp-6: Relativistic Quantum Mechanics |