**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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