Question Paper

Unit-1
Wave mechanics

|Q.1 |Show that the phase velocity of de-Broglie wave is greater than the velocity of light. |
|Q.2 |State and explain Heisenberg uncertainty principle. Using this principle show that the electron cannot reside in the nucleus of an atom. |
|Q.3 |Prove that group velocity is equal to the velocity of the particle with which the waves are associated. |
|Q.4 |Distinguish between phase velocity (Vp) and group velocity (Vg) of a wave packet. Prove that Vg.Vp = C2 |
|Q.5 |Write short notes on wave particle duality with an example of suitable experiment. |
|Q.6 |Derive time dependent Schrödinger’s equation for matter waves. |
| |OR |
| |Derive the time dependent equation for steady state wave function. |
|Q.7 |Derive time Independent Schrödinger wave equations and interpret the solution in terms of wave functions. |
|Q.8 |A particle is in motion along a line x= 0 and x = a, with zero potential energy. At points for which x < 0 and x < a potential energy is |
| |infinite. Solving Schrödinger’s equation, obtain energy Eigen values and normalized wave function for the particle. |
|Q.9 |Give physical interpretation of wave function ψ. |
|Q.10 |Prove that the result of phase and group velocity is true for electromagnetic waves in a homogenous medium.