Syllabus

Module 1: (8 Hours)
Formalism of quantum mechanics: Hilbert space and wave function, Dirac bra-ket notations, operators, commutation algebra, uncertainty relation between operators and its significance, function operators, inverse and unitary operators, Eigenvalues and Eigenvectors of an operator, infinitesimal and finite unitary transformations.

Module 2: (8 hours)
Matrix representation: representation of kets, bras, and operators both in discrete and continuous basis, change of bases and unitary transformation, matrix representation of Eigen-value problem, position and momentum operators and its connections in continuous basis, parity operator, wave and matrix mechanics.

Module 3: (10 hours)
Postulates of quantum mechanics: state of a system, probability density, superposition principle, observables and operators, measurement in quantum mechanics, expectation values, complete sets of commuting Operators, measurement and the uncertainty relations. Time Evolution Operators: stationary states, conservation of probability, time evolution of expectation values, infinitesimal and finite unitary transformations, symmetries and conservation laws, connecting quantum to classical mechanics.

Module 4: (10 hours)
Angular momentum: general formalism of angular momentum, orbital and spin angular momentum, matrix representation of angular momentum, experimental evidence of spin, Stern-Gerlach experiment, spin half particles and Pauli matrices, brief review on application of Schrodinger equation to one dimensional problems, applications to three dimensional harmonic oscillator and central potential.

Module 5 (12 hours)
Rotations and addition of angular momenta: rotation in classical and quantum physics, addition of two angular momentum, calculation of Clebsch-Gordan coefficients, coupling of orbital and spin angular momenta, rotation matrices for coupling two angular momenta, isospin, scalar, vector, and tensor operators, reducible and irreducible tensors, Wigner–Eckart theorem for spherical tensor operators.

Get familiar with the formulation of Quantum Mechanics through linear algebra and matrix algebra.

Learn about the matrix algebra for kets, bras, and operators.

To learn about the eigen energies and functions and solving problems in quantum mechanics.

To get the idea of spin and orbital angular momentum and solving problems in more than one dimensional problem.

5. To understand the addition of angular momentum and solving problems.

At the end of the course, students will be able to:
CO1: Understand and formalize quantum mechanics through linear algebra and Hilbert space.

CO2: Use Dirac bra-ket notations in formulating quantum mechanics.

CO3: Solve quantum mechanical problems to obtain Eigenvalues and Eigen states.

CO4: Visualize and get a clearer picture of spin and orbital angular momentum.

CO5: Apply principles of angular momentum addition in advanced courses.

N. Zettili, Quantum Mechanics: Concepts and Applications, Wiley , 2nd Edition (2009).

D. J. Griffith and D. F. Schroeter, Introduction to Quantum Mechanics, Cambridge University press , 3rd Edition (2018).

C. Cohen-Tannoudji, Bernard Diu, Frank Laloe, Quantum Mechanics, Volume 1: Basic Concepts, Tools, and Applications, John Willey-VCH , 2nd Edition (2019).

J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, Cambridge University Press , 3rd Edition (2020).