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Questions:

1. Write the significant properties of a wave function.
2. Explain Dirac's Bra and Ket notations.
3. Show that [x, p_] = ih.
4. What are degenerate and non-degenerate states?
5. Show that for Pauli spin matrices sigma_2 == sigma_x^2 + sigma_y^2 + sigma_z^2 = 3.
6. Derive Schrodinger's time independent and time dependent equation for matter waves.
7. Explain Heisenberg uncertainty principle.
8. Solve the Schrdinger equation for a rigid rotator with free axis.
9. Prove that product of two commuting projection operators p and pz is also a projection operator.
10. Show that L^2 = L_x^2 + L_y^2 + L_z^2.
11. If sigma_x, sigma_y, and sigma_z are Pauli spin matrices and A and B are constant vectors, show that (sigma.A)(sigma.B) = A.B + i sigma.(A x B).
12. Discuss perturbation theory for non-degenerate levels.
13. Show that for ground state of hydrogen atom there is no first order Stark effect.
14. Write down Schrdinger wave equation for particle and solve it and find reflection and transmission coefficients for case E < V, where E is total energy of particle.
15. Solve the radial part of Schrodinger equation for Hydrogen atom and obtain energy eigenvalues.
16. Use matrix method to obtain the eigenvalues of harmonic oscillator with Hamiltonian H = p^2 + kx^2.
17. Give the theory of first order Stark effect on the basis of quantum mechanics and discuss the splitting of the energy levels.