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3. L. D. Landau and E. M. Lifshitz, Mechanics 3rd ed. (Pergamon).
4. R. G. Takwale& P. S. Puranik, Introduction to Classical Mechanics (Tata McGraw –Hill)
5. Kiran C. Gupta, Classical Mechanics of Particles and Rigid Bodies (Wiley Eastern).
6. N. C. Rana and P. S. Joag, Classical mechanics (TMH).

Phys.412 Quantum Mechanics 3+1*

LEARNING OBJECTIVES:

The primary aim of this course is to:
• make students aware about the basic formulations in quantum mechanics.
• There are many different types of representations of state and operators that are very
useful in studying the subject deeply.
• The course takes up the responsibility to give information about hermitian operators, their
eigenvalues and eigenvectors. It teaches about various commutation and uncertainty
relations.
• Students will be given knowledge about unitary transformations, dirac delta function,
matrix representation of operators and their applications.
• Main focus is on angular momentum operator and their representation in spherical
coordinates. Addition of angular momenta is also taught.
• Students will be given insight to solve Schrodinger wave equation in three dimensions.
• Basic idea of time independent perturbation theory is provided.

LEARNING OUTCOMES:

After completion of course, students will able to
 Learn the basic concepts of matrix algebra in quantum mechanics.
 Understand Hilbert space, concepts of basis and operators, Dirac, bra and ket notations.
 Understand the theory of orbital and spin angular momentum, tensor operators, CG
7. coefficients and Wigner Eckart theorem.
 To understand time independent and dependent perturbation theory.
 To apply time independent and dependent perturbation theory to non-degenrate and
8. degenerate systems.
 Make use of variation principle to ground state of helium atom.

THEORY (45 Hours)

UNIT 1 (15 Hours)

Matrix formulation of Quantum Mechanics:Matrix Algebra: Matrix addition and multiplication,
Null unit and Constant Matrices, Trace,Determinant and Inverse of a Matrix, Hermitian and
unitary Matrices, Transformation anddiagonalization of Matrices, Function of Matrices and
matrices of infinite rank. Vectorrepresentation of states, transformation of Hamiltonian with
unitary matrix, representation of anoperator, Hilbert space. Dirac bra and ket notation, projection
operators, Schrodinger, Heisenberg and interaction pictures. Relationship between Poisson
brackets and commutationrelations. Matrix theory of Harmonic oscillator.

UNIT 2 (15 Hours)
Symmetry in Quantum Mechanics:Unitary operators for space and time translations. Symmetry
and degeneracy. Rotation andangular momentum; Commutation relations, eigenvalue spectrum,
angular momentum matricesof J +, J-, Jz, J2. Concept of spin, Pauli spin matrices. Addition of
angular momenta, Clebsch-Gordon coefficients and their properties, recurssion relations. Matrix
elements for rotated state,irreducible tensor operator, Wigner-Eckart theorem. Rotation matrices

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