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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....
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