N A L A N D A O P E N U N I V E R S I T Y
M.Sc. Physics, Part-I
PAPER-II
(Quantum Mechanics)
Annual Examination, 2016
Time 3 Hours. Full Marks 80
Answer any Five Questions.
All questions carry equal marks.
1. State and prove Heisenberg's uncertainty principle. What are its consequences.
2. State the postulates of Schrödinger formulation of quantum mechanics.
3. Give a brief account of quantum mechanical theory of Stark effect for splitting of energy levels
of hydrogen atom.
4. State the hypothesis of de Broglie. Derive the de Broglie relation for a photon from the
principle of mass-energy equivalence.
5. Set up Schrödinger equation for an one dimensional harmonic Oscillator and solve it to find the
energy eigenvalues and eigenfunctions.
6. Using perturbation theory find the energy levels and energy eigenfunctions for the matrix correct upto first order in . Compare these energy eigenvalues
with the exact one i.e. by diagonalizing the matrix H.
7. Write down Schrödinger's wave equation for hydrogen atom and apply the separation of
variables method to obtain the radial wave function for the system.
8. What is an operator Explain the use of matrix representation of operatiors in quantum
mechanics. What are unitary and Hermitian operators
9. Using the method of partial waves for the study of scattering problems. Show that total
10. Write short notes on any Two of the following
Dirac delta function.
Expectation values.
Ehrenfest's theorem.
Bra nad Ket notations.