PH 204

Quantum Mechanics-I

2-1-0-6

 

Syllabus:

Basic principles of quantum mechanics: Heisenberg Uncertainty principle; Introduction to linear vector spaces: bra and ket vectors, completeness, orthonormality, basis vectors, Orthogonal, Hermitian and Unitary operators, change of basis, Eigenvalues and expectation values, position and momentum representation

Postulates of Quantum Mechanics: Wave particle duality, wave function and its relation to the state vector, probability and probability current density, conservation of probability, equation of continuity, Schrödinger equation

Simple potential problems: infinite potential well, step and barrier potentials, finite potential well and bound states; Linear harmonic oscillator, operator algebra of harmonic oscillator, coherent states and their properties

Three dimensional problems: spherical harmonics, free particle in a spherical cavity, central potential, Three dimensional harmonic oscillator, degeneracy, Hydrogen atom

Angular momentum: Commutation relations, spin angular momentum, Pauli matrices, raising and lowering operators, L-S coupling, Total angular momentum, addition of angular momentum, Clebsch-Gordon coefficients; The spin-orbit coupling and its consequences, charged particle in a uniform magnetic field

 

Texts:

  1. R. Shankar, Principles of Quantum Mechanics, Springer (India) (2008).
  2. D. J. Griffiths, Introduction to Quantum Mechanics, 2nd Ed., Pearson Education (2005)
  3. P. W. Mathews and K. Venkatesan, A Textbook of Quantum Mechanics, Tata McGraw Hill (1995).

References:

  1. J. Sakurai, Modern Quantum Mechanics, Pearson Education (2002).
  2. F. Schwabl, Quantum Mechanics, Narosa (1998).
  3. L. Schiff, Quantum Mechanics, Mcgraw-Hill (1968).
  4. E. Merzbacher, Quantum Mechanics, John Wiley (Asia) (1999).
  5. Ajit Kumar, Fundamentals of Quantum Mechanics, Cambridge University Press (2018).