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

Curriculum

Subject: Quantum Mechanics- I

Subject Code: 09020103

S. No.

Topic

Learning Objective

Teaching guidelines

Methodology

Time (Hrs)

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
To understand the central concepts and principles of quantum mechanics: the Schrödinger equation, the wave function and its physical interpretation, stationary and non-stationary states, time evolution and expectation values. To cover 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,cTunneling problem and Linear Harmonic Oscillator
  • Lecture.
  • Seminar.
  • Discussion/Interaction with Students.
  • Assignment.
  • Discussion on Assignment.         Evaluation of Assignment

 

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.
To explain why wave functions and operators in quantum mechanics need to satisfy specific mathematical requirements. Further, understand the role of uncertainty in quantum physics, and use the commutation relations of operators to determine whether or not two physical properties can be simultaneously measured. To cover 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.
  • Lecture.
  • Seminar.
  • Discussion/Interaction with Students.
  • Assignment.
  • Discussion on Assignment.         Evaluation of Assignment

 

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.
To interpret the wave function and apply operators to it to obtain information about a particle’s physical properties such as position, momentum and energy. To cover 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.
  • Lecture.
  • Seminar.
  • Discussion/Interaction with Students.
  • Assignment.
  • Discussion on Assignment.         Evaluation of Assignment

 

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.
To analyze more complicated quantum
phenomena with advanced techniques and explore modern
applications of quantum theory.
To cover 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.
  • Lecture.
  • Seminar.
  • Discussion/Interaction with Students.
  • Assignment.
  • Discussion on Assignment.         Evaluation of Assignment

 

10

Reference Books:
1. Schiff. Quantum Mechanics. New Delhi: Tata McGraw-Hill.
2. B. Craseman and J.L. Powell. Quantum Mechanics. New Delhi: Narosa.
3. S. Gasiorowicz. Quantum Mechanics. New York: John Wiley.
4. J.J. Sakurai. Modern Quantum Mechanics. Addison Wesley.
5. P.M. Mathews and K. Venkatesan. Quantum Mechanics. New Delhi: Tata McGraw-Hill.
6. Ghatak and Loknathan. Quantum Mechanics.
7. M.P. Khanna. Quantum Mechanics. New Delhi: HarAnand.
8. V.K. Thankappan. Quantum Mechanics. New Delhi: New Age International.
9. N. Zettili. Quantum Mechanics: Concepts and Applications.
10. Bransden and Jochain. Quantum Mechanics.
11. Satyaprakash. Quantum Mechanics.