PHYS-5011:Mathematical-Physics-III

MAJOR-V: PHYS5011: MATHEMATICAL PHYSICS-III

Practical: 30 Hours

Experiments:

Scilab/ Python based Simulations Experiments on Problems:

1. Compute the Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) of the function $e^{-x^2}$ given in tabulated form.[Notes/Codes]

2. Perform circuit analysis of a general LCR (resistor, inductor, capacitor) circuit using Laplace’s transform. [Notes+Codes]

3. Solve KCL (Kirchhoff's Current Law) and KVL (Kirchhoff's Voltage Law) in a circuit using Laplace transform. [Notes+Codes]

4. Find the charge and the current in a series LCR (resistor, inductor, capacitor)circuit using Laplace transform. [Notes+Codes]

5. Write a program to multiply any two 3 x 3 matrices. [Matrix Notes/Codes]

6. Write a program to find the inverse of a 3 x 3 matrix. [Matrix Notes/Codes]

7. Find the eigenvalues and the eigenvectors of a 3 x 3 matrix and the same for Pauli spin matrices. [Matrix Notes/Codes]

8. Determine the principal axes of inertia by diagonalizing the inertia tensor.

9. Define the position operator $\hat{x}$ and momentum operator $\hat{p}$ in the position representation and calculate the value of the commutator $[\hat{x}, \hat{p}]$.

10. Estimate the ground state energy and wave function of a quantum system using the variational method.

11. Study of geodesics in Euclidean and other spaces.