PH101: Physics I (2-1-0-6)

Calculus of variation: Fermat’s principle, Principle of least action, Euler-­Lagrange equations and its applications. Lagrangian mechanics: Degrees of freedom, Constraints and constraint forces, Generalized coordinates, Lagrange’s equations of motion, Generalized momentum, Ignorable coordinates, Symmetry and conservation laws, Lagrange multipliers and constraint forces. Hamiltonian mechanics: Concept of phase space, Hamiltonian, Hamilton’s equations of motion and applications.

Special Theory of Relativity: Postulates of STR. Galilean transformation. Lorentz transformation. Simultaneity. Length Contraction. Time dilation. Relativistic addition of velocities. Energy momentum relationships.

Quantum Mechanics: Two-­‐slit experiment. De Broglie’s hypothesis. Uncertainty Principle, wave function and wave packets, phase and group velocities. Schrödinger Equation. Probabilities and Normalization. Expectation values. Eigenvalues and eigenfunctions.
Applications in one dimension: Infinite potential well and energy quantization. Finite square well, potential steps and barriers -­‐notion of tunnelling, Harmonic oscillator problem zero point energy, ground state wavefunctionand the stationary states.

Texts/References:

1. Introduction to Classical Mechanicsby Takwale R and Puranik P (McGraw Hill Education, 1 st Ed., 2017)
2. Classical mechanics by John Taylor (University Science Books, 2005)
3. Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particlesby R. Eisberg and R. Resnick (John-­‐Wiley, 2 nd Ed., 2006)