1800 102 5661 info@sgtuniversity.org

M.Sc. (Physics) | Subject: Quantum Mechanics- I | Subject Code: 09020103

Syllabus

Subject: Quantum Mechanics- I

Subject Code: 09020103

S.N

Topic

Domain

Hours as per UGC

1

GENERAL FORMALISM OF QUANTUM  & SCHROEDINGER EQUATIONS WITH APPLICATIONS

  • The Schrödinger equations
  • Time dependent and time independent forms,
  • Probability current density, expectation values, Ehrenfest’s theorem,
  • Gaussian wave packet and its spreading.
  • Exact statement and proof of the uncertainty principle,
  • Eigen values and Eigen functions,
  • wave unction in coordinate and momentum representations,
  • Degeneracy and orthogonality.
  • Application of Schrodinger equation for a particle in one dimensional Box,
  • Tunneling problem and Linear Harmonic Oscillator

Must Know

10

2

QUANTUM OPERATORS

  • Operator in quantum mechanics
  • Hermitian operator and Unitary operator change of basis,
  • Eigen values and eigenvectors of operators,
  • Dirac s Bra and Ket algebra,
  • Linear harmonic oscillator, coherent states,
  • Time development of states and operators,
  • Heisenberg, Schroedinger and interactive pictures,
  • annihilation & creation operators,
  • Matrix representation of an operator,
  • Unitary transformations.

Must know

10

3

ANGULAR MOMENTUM

  • The angular momentum operators and their representation in spherical polar coordinates,
  • solution of Schrodinger equation for spherically symmetric (central) potentials,
  • spherical harmonics,
  • Hydrogen atom.
  • Commutators and various commutation relations.
  • Eigen values and eigenvectors of L2 and Lz. Spin angular momentum,
  • Eigen values and eigenvectors of J2 and Jz.
  • Representation of general angular momentum operator,
  • Addition of angular momentum, C.G. coefficients,
  • Stern-Gerlach experiment.

Must know

Nice to know

10

4

TIME INDEPENDENT PERTURBATION THEORY

  • Time independent perturbation theory
  • Nondegenerate case,
  • first and second order perturbation,
  • Degenerate case,
  • First order Stark effect in hydrogen.
  • The Variational Method: expectation value of the energy,
  • application to the ground state of Harmonic oscillator,
  • Hydrogen atom and
  • Helium atom,
  • Vander-Waals interactions.

Must know

Nice to know

10

Reference Books:

  • Schiff. Quantum Mechanics. New Delhi: Tata McGraw-Hill.
  • B. Craseman and J.L. Powell. Quantum Mechanics. New Delhi: Narosa.
  • S. Gasiorowicz. Quantum Mechanics. New York: John Wiley.
  • J.J. Sakurai. Modern Quantum Mechanics. Addison Wesley.
  • P.M. Mathews and K. Venkatesan. Quantum Mechanics. New Delhi: Tata McGraw-Hill.
  • Ghatak and Loknathan. Quantum Mechanics.
  • M.P. Khanna. Quantum Mechanics. New Delhi: HarAnand.
  • V.K. Thankappan. Quantum Mechanics. New Delhi: New Age International.
  • N. Zettili. Quantum Mechanics: Concepts and Applications.
  • Bransden and Jochain. Quantum Mechanics.