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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
M.Sc.DEGREE EXAMINATION PHYSICS
SECONDSEMESTER APRIL 2018
PH 2812- MATHEMATICAL PHYSICS
Date: 25-04-2018 Dept. No. Max. 100 Marks
Time: 01:00-04:00
Part A
Answer ALL questions (10 x 2
1. Check whether is analytic or not.
2. State Taylor's theorem.
3. Define Dirac Delta function. What is its Laplace transformation?
4. State convolution theorem.
5. Find
6. Define inverse Fourier cosine and sine transformation.
7. Write the orthonormal property of Legendre polynomials.
8. State the condition for which the differential equation is Sturm-Liouville type.
9. Distinguish between Abelian group from cyclic group.
10. What is homomorphism?
Part
Answer any FOUR questions x 7.5 30)
11. State and prove Cauchy's theorem.
12. Solve the initial value problem by the Laplace transform.
13. Solve two-dimensional wave equation.
14. Obtain Fourier expansion for the function,
15. Derive the recurrence relations

16. Develop transformation matrix for rotation operation. Predict the number of rotational and vibrational modes of linear molecule CO2.
Part
Answer any FOUR questions x 12.5 50)
17. Find the Taylor's series to represent when
Derive Cauchy-Riemann equation for a function to be analytic.
2
18. Evaluate
is an analytic function and find
19. Obtain the general solution of partial differential equation with the boundary condition
20. Derive the orthogonality relation for Laguerre's polynomials.
21. Obtain the transformation matrices of the symmetry elements for the axis of symmetry and ii) for the improper axis of symmetry
Enumerate and explain the symmetry elements of H2O and NH3 molecules.
22. Solve Legendre's differential equation by Frobenius power series method.