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# Physics - I

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

**Prerequisite**: Nil

**Calculus of variation:** Fermats 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. Schrodinger 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 wavefunction and the stationary states.

*Texts:*

- R. Takwale and P. Puranik, Introduction to Classical Mechanics, 1st Edition, Mc-Graw Hill Education, 2017.
- John Taylor, Classical mechanics, University Science Books, 2005.
- R. Eisberg and R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, 2nd Edition, John-Wiley, 2006.

*References:*

- Patrick Hamill, A Students Guide to Lagrangians and Hamiltonians, Cambridge University Press, 1st edition, 2013.
- M. R. Spiegel , Theoretical Mechanics, Tata McGraw Hill, 2008.
- R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Volume I, Narosa Publishing House, 1998.
- R. Resnick, Introduction to Special Relativity, John Wiley, Singapore, 2000.
- S. Gasiorowicz, Quantum Physics, John Wiley (Asia), 2000.