 # Office of Academic AffairsIndian Institute of Science Education and Research Bhopal

Physics

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)