Quantum Mechanics: Important part-B questions

ANNA UNIVERSITY PART B QUESTIONS

1. Arrive at the Schrodinger wave equation and apply the same for a particle in a rectangular box to obtain the energy eigen values and the corresponding eigen functions.

2. Arrive at the time independent Schroedinger's wave equation and explain the significance of the wave function ᴪ.

3. Derive in time dependent Schroedinger wave equation and hence deduce the time independent Schroedinger wave equation.

4. Solve Schroedinger wave equation for a particle in a box (one dimensional) and obtain the energy eigen values.

5. Derive an expression for energy levels of a particle enclosed in one‒dimensional potential box of width 'a' and infinite (∞) height.

6. Deduce Schrondinger's time dependent and time independent equations.

7. Derive the time‒dependent (1‒D) Schroedinger equation from fundamentals.

8. (i) Explain the application of Schrodinger wave equation to one dimensional potential well.

(ii) List out the physical significance of the wave function ᴪ.

9. Arrive at the Schrodinger wave equation and apply the same for a particle in a rectangular box to obtain the energy eigen values and the corresponding eigen functions.

10. Derive Schroedinger equation for a particle in three dimensional box. Determine the eigen values and eigen functions for the same.

11. (1) Write short notes on tunnelling effect.

(ii) Describe the principle, construction and working of scanning tunnelling microscope.

12. Determine the energy of a particle confined in one dimensional potential well and find the normalization of wave function to study the behaviour inside the potential well.

13. Discuss the normalization and probability interpretation of a wave function.

14. Explain the de‒Broglie concept of matter waves and hence derive an expression for de‒broglie wavelength.

ADDITIONAL PART B QUESTIONS

1. What is meant by black body radiation.

2. (i) What are the draw backs of classical free electron theory.

(ii) Explain the de‒Broglie concept of wave nature.

(iii) Derive Schroedinger time dependent and time independent wave equations.

3. (i) What are matter waves? Give its properties.

(ii) Obtain the de‒Broglie wavelength in terms of momentum, energy and temperature.

4. With the quantum concepts, explain the energy level of an electron enclosed in an infinitely deep one dimensional potential box.

5. Derive the schroedinger time independent wave equation for a free particle enclosed in a one dimensional potential well of length 'a' with infinite potential barriers and get the normalised wave function for the free particle.

6. Based on quantum physics, show that the energy levels of an electron are discrete.

7. Arrive at the Eigen valves and Eigen functions for an electron enclosed in a one dimensional potential box and extend the same for a three dimensional box.

8. What is meant by photo‒electric effect? Deduce an expression for Einstein's photo‒electric equation and discuss its special cases.

9. Describe the barrier penetration process and quantum tunnelling of an electron.

10. Derive the transmission and reflection coefficients for a particle which undergoes quantum tunnelling.