New Question Collection

Candidates are required to give answers in their own words as far as practicable.
Attempt ALL the questions.
1. Describe Davisson-Germer experiment. Interpret the result of this experiment. Explain the limitations of this famous and important experiment. [6+2+2]
OR
Set up time-independent Schrodinger wave equation in spherical polar coordinates. Explain the importance of this equation in physics. [8+2]
2. Explain cold emission of electrons in a metal and find expression for the transmission coefficient by assuming sufficiently smooth potential barrier. Describe the importance of cold emission of electrons.
[8+2]
OR
Set up Hamiltonian for two interacting particles in spherical polar coordinates. Write Schrodinger equation for this Hamiltonian in terms of angular momentum operator. Discuss the translational, rotational kinetic energies and kinetic energy of rotation. [5+3+2]
3. What do you mean by observables in quantum mechanics? Find equation of motion for an observable and explain the principle of first quantization. [2+6]
4. What do you mean by the commuting and non-commuting operator. Explain with two examples.
[4+4]
5. Express Hamiltonian of a one-dimensional harmonic oscillator in terms of creation and annihilation operator. [8]
6. Solve the Schrodinger equation to obtain radial part of the wave function for V(r) = 0. [8]
7. Answer all questions. [3x2=6]
a) Explain non-interacting coupled harmonic oscillator.
OR
Describe possible shapes of the orbital for l = 1.
b) Show that the linear momentum is not quantized.
OR
Describe two examples of even and odd parity states.
8. Answer all questions. [3x4=12]
a) Explain spherical potential well of finite depth.
b) What do you mean by the normalization of the wave function?
c) Is there any similarity between parity and projection operator? Explain.
d) Describe conservation of probability
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