Office of Academic Affairs
Indian Institute of Science Education and Research Bhopal
PHY 303: Quantum Mechanics I (4)
Learning Objectives:
The course will lay down foundations of quantum mechanics via wave-particle duality, uncertainty principle and Schrodinger's equation. Operator formalism will be developed and applied to various problems in one-dimensional potential and central potential. Particularly, hydrogen atom problem and angular momentum algebra be discussed in detail.
Course Contents:
Need for Quantum Theory: (Brief review of PHY 201)
Particle nature of elctromagnetic wave: Photoelectric effect; Blackbody radiation (Rayleigh-Jeans Law); Compton effect Wave properties of particle: Electron diffraction Discrete energy levels: Bohr atom
Schrodinger Equation: Uncertainty Principle; Probability interpretation and probability current; Coordinate and momentum representations; Expectation values of dynamical variables; Descriptions of wave packets and its evolution
Principles of Quantum Mechanics: Hermitian operators; Eigenvalues; vector spaces; Classical limit – Ehrenfest’s theorem; Stationary states
One Dimensional Problem: Harmonic Oscillator – creation and annihilation operators; Brief descriptions of potential step, barrier and well (already covered in PHY 201) – Ideas of bound states, scattering states and resonances; Dirac-delta potential, Applications to alpha-decay
Formalism: Generalized uncertainty principle; Simultaneous eigenstates of commuting operators; Introduction to Dirac’s notation. Theory of Angular Momentum: Orbital angular momentum and eignevalue problem; Spherical harmonics, Spin angular momentum, addition of angular momentum
Central Potential: Bound states in three dimensions; Hydrogen atom
Charged particle in Electromagnetic field: Gauge invariance of Schrodinger equation; Larmor frequency; Brief discussions on normal and anomalous Zeeman effect (Further details in Atomic and Molecular Physics course, PHY 402); Landau levels
Foundational Issues: Measurements and interpretations of Quantum Mechanics; Bell’s inequality; EPR paradox
Suggested Books:
- H. C. Verma, Quantum Physics (Surya Publn)
- R. P. Feynman, R. B. Leighton and M. Sands, The Feynman Lecture of Physics Vol 3 (Narosa Publ.)
- J. J. Sakurai, Modern Quantum Mechanics (Pearson)
- B. H. Bransden and C. J. Joachain, Quantum Mechanics 2nd Ed (Pearson Education)
- D. J. Griffiths, Introduction of Quantum Mechanics, 2nd Ed. (Pearson)
- P. A. M. Dirac, The Principles of Quantum Mechanics. (4th Ed. Oxford Science Publications)
- C. Cohen-Tannoudji, Quantum Mechanics, (Vol I and II) (John Wiley and Sons)
- R. Shankar, Principles of Quantum Mechanics, 2nd Ed (Springer)
- A. I. M. Rae, Quantum Mechanics, 4th Ed. (IOP publishing)
- E. Merzbacher, Quantum Mechanics , 3rd Ed. (Hamilton Printing Company)
- L. D. Landau and L. M. Lifshitz, Quantum Mechanics Non-Relativistic Theory. 3rd Ed. (Butterworth-Heinemann)
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