Course Instructor: Dr. Camelia Das
Text Books:
1. T1: Introduction to Quantum Mechanics, David J. Griffiths, Second Edition, Pearson Education.
2. T2: Perspective of Quantum Mechanics, S. P. Kuila, New Central Book Agency (P) Ltd.
Reference Books:
1. R1: Quantum Mechanics: concepts and applications, Nouredine Zettili, Second edition Wiley.
Learning Objective: Newtonian mechanics was found to be inadequate in the early years of this century- it’s all right in “everyday life”, but for objects moving at high speeds (near speed of light) it is incorrect, and must be replaced by special relativity (introduced by Einstein in 1905); for the objects that are extremely small (near the size of atom) it fails for different reasons, and is superseded by quantum mechanics (developed by Bohr, Schrödinger, Heisenburg, and many others). For objects that are both very fast and very small (as in common in modern physics), a mechanics that combines relativity and quantum principles is in order: this relativistic quantum mechanics is known as quantum field theory.
Learning Outcome: The student should have the following learning outcomes after completion of the course:
- the time-dependent and time-independentSchrödinger equation for simple potentials like for instance the harmonic oscillator and hydrogen like atoms, as well as the interaction of an electron with the electromagnetic field
- quantum mechanical axioms and the matrix representation of quantum mechanics
- approximate methods for solving the Schrödinger equation ( the variational method, perturbation theory, Born approximations)
Application of Schrödonger equation to One dimensional Problem- Free States: Boundary Condition of surface of finite potential , Boundary condition of surface of infinite potential, A single step potential, One dimensional rectangular potential barrier (quantum mechanical tunneling effect), Application of a barrier penetration (α decay), One dimensional square well potential
Application of Schrödonger equation to One dimensional Problem-Bound State: The Particle in a box, One dimensional square well potential for infinite depth, One dimensional square well potential for finite depth, The Harmonic Oscillator, Ladder Operator, The delta function potential,
Quantum Mechanics in three dimensions: Free Particle in three dimensions, Particle in a three dimensional rectangular box, Three dimensional harmonic oscillator (Cartesian coordinates) , Spherical Harmonics, The Hydrogen Atom,
Angular Momentum and Spin: The Operator method for solving Angular Momentum problems, Eigen values and Eigenfunction of Lz and L2, Spin angular momentum, Pauli’s Theory of spin, Total Angular momentum operator, Eigenvalues of Jz and J2, Eigenvalues of J+ and J-, Eigenvalues of Jx and Jy, Angular Momentum Matrices, Eigenfunction of Jz and J2
- Teacher: Camelia Das