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Paper : Quantum Mechanics – II

Code: 09020202

Sr. No.



Hours as per UGC

1. 1.WKB Approximation for one dimensional problem,
2. WKB Approximation for three dimensional problem,
3. Application to barrier penetration.
4.Time dependent perturbation Theory
5.General expression for the transition probability from one state to another,
6. Harmonic perturbation,
7.Fermi’s Golden rule, selection rules,
8.Adiabatic and sudden approximations
Must  Know 10 hrs
2. 1.General considerations; kinematics, wave mechanical picture, scattering amplitude,
2.Differential and total cross-section
3.Green’s function for scattering
4.Partial wave analysis: asymptotic behaviour of partial waves, phase shifts, scattering amplitude in terms of phase shifts, cross-sections
5. Optical theorem.
6.Phase shifts and its relation to potential
7. Effective range theory.
8.Application to low energy scattering; resonant scattering
9.Breit-Wigner formula for one level and two levels,
10.Non-resonant scattering-wave and p-wave resonances
11. Exactly soluble problems; Square-well, Hard sphere, coulomb potential.
12. Born approximation; its validity, Born series.
Must   Know






Must Know

10 hrs
3. 1.Many-particle Schrodinger wave equation
2.Identical particles: Physical meaning of identity
3.Principle of in-distinguishability and its consequences
4. Exchange operator, Symmetric and anti-symmetric wave functions 5.Connection between spin, symmetry and statistics 6.Fermions and bosons; Spin and total wave function for a system of two spin particles
7.Pauli exclusion principle and Slater determinant
8.Application to the electronic system of the helium atom (para- and orthohelium).
Must Know 10 hrs
4. 1.Klein-Gordan Equation,
2.Dirac Equation and its plane wave solution.
3.Transition probability for absorption
4.Transition probability for induced emission,
5.Electric dipole
6.Forbidden transitions
7. Selection rules.
Must Know 10 hrs

References Books
1. Quantum Mechanics (3rd edition) by L. I. Schiff
2. Quantum Mechanics (2nd edition) by B. H. Bransden and Joachain
3. Introduction to Quantum Mechanics (2nd edition) by David J. Griffiths
4. Quantum Mechanics by A. K. Ghatak and S. Loknathan
5. A Textbook of Quantum Mechanics by P. M. Mathews and K. Venkatesan
6. Quantum Mechanics (3rd edition) by S. Gasiorowicz