P HY 50 3: Quantum Mechanics I 3 CH (45L+15T)

M.Sc. (Physics) curriculum, Tribhuvan University 2073

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PHY503: Quantum Mechanics I 3 CH (45L+15T) Nature of the course: Theory Full Marks: 75 Pass Marks: 37.5 Course Description:

This course contains a description and formulation of quantum mechanics. Course Objectives:

The objective of this course is to provide the students with adequate knowledge of non-relativistic quantum mechanics and enable them to apply the knowledge to study the atomic, molecular and other mechanical systems.

Course Contents:

1. Mathematical Tools of Quantum Mechanics: [12 hours] 1.1 One particle wave function space: vector space, scalar product, linear operator, closure

relation, 1.2 Discrete and continuous bases, 1.3 State space, Dirac notation: ket and bra vectors, duel space, correspondence between

ket and bra, 1.4 Projection operator, Hermitian conjugation 1.5 Representation in state space: orthonormalization relation, closure relation, 1.6 Matrix representations of kets, bras, operators, change of representations, 1.7 Eigenvalue equations, 1.8 Observables: definition of an observable, the projectors, 1.9 Sets of commuting observables, complete sets of commuting observables.

2. Postulates of Quantum Mechanics: [6 hours]

2.1 Statement of the postulates, 2.2 Physical interpretation, 2.3 Physical implications of the Schrodinger equation, 2.4 Conservation of probability, 2.5 Equation of motion for an observable, 2.6 Schrodinger, Heisenberg and Interaction pictures.

3. Revisions of Barriers and Bound States in One Dimension: [4 hours]

3.1 Double well model of a molecule, 3.2 Kronig-Penny model for metals.

4. Spin and Magnetic Moment: [10 hours]

4.1 Revision of angular momentum, ladder operators in spherical coordinates 4.2 Need for matrix representation of spin, 4.3 Pauli spin matrices, 4.4 Spinors and expectation values, 4.5 Pauli operators, 4.6 Magnetic moment of an electron: precession of an electron in a magnetic field, 4.7 Magnetic resonance 4.8 Space inversion and time reversal, 4.9 Isospin.

M.Sc. (Physics) curriculum, Tribhuvan University 2073

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5. Addition of Angular Momenta: [8 hours] 5.1 Addition of two spins, 5.2 Addition of two angular momenta: general method, 5.3 Vector operators: Wigner-Eckart theorem, 5.4 Identical particles and symmetry, 5.5 Nuclear Forces.

6. Stationary Perturbation theory: [5 hours]

6.1 Perturbation theory 6.2 Non-degenerate case 6.3 Simple applications 6.4 Degenerate case, Simple cases of removal of degeneracy 6.5 Exchange degeneracy 6.6 Rayleigh Ritz Variation Method

Text Books:

1. Agrawal, B.K. & Prakash, H. – Quantum Mechanics, Prentice Hall of India, New Delhi (1997).

2. Cohen-Tannoudji, C, Duui. B. & Laloe, F. – Quantum Mechanics, Vol. I & II, John Wiley

(1977).

Reference Books:

1. Schiff, L. I.- Quantum Mechanics, 3rd ed., Tata McGraw Hill, Delhi (1968).

2. Landau, L.D., Lifshitz E.M. – Quantum Mechanics: Non-Relativistic Theory, Vol. 3 (3rd ed.).

Pergamon Press (1977).

3. Merzbacher, E. - Quantum Mechanics, 2nd ed., John Wiley, New York (1969).

4. Messiah, A. - Quantum Mechanics, John Wiley, New York (1963).

5. Thankappan, V. K. - Quantum Mechanics, Wiley Eastern Ltd., New Delhi (1993).