**EXERCISES**

1. Differentiate between ‘phase velocity’ and ‘group velocity’.

(Amity Univ., Noida, May 2005)

2. What are de Brogile waves? Show that the velocity of matter waves is found to be greater than the velocity of light.

(Amity Univ., May 2005)

3. What are the aim of Davisson Germer’s experiment? Describe the experiment and show how far was it successful.

(Amity Univ., May 2006)

4. Show that the de Brogile wavelength of a particle of rest mass m_{0} and kinetic energy T is given by

(Amity Univ., May 2006)

5. What do you understand by phase velocity and group velocity? How is the group velocity of wavepacket associated with a particle related to the particle velocity?

(Amity Univ., May 2006)

6. State Heisenberg’s uncertainty principle and describe an experiment to prove it.

(Amity Univ., May 2006, May 2005)

7. What is Born’s interpretation of wave function?

(Amity Univ., May 2005)

8. What are ‘operators’ in quantum mechanics? Write down the formulae for

a. momentum operator, and

b. kinetic energy operator with reference to a one-dimensional function.

(Amity Univ., May 2005)

9. What do you understand by

a. eigen values and eigen functions of an operator

b. expectation value of a dynamical variable.

(Amity Univ., May 2006)

10. What is de Brogile principle?

11. Which considerations led de Brogile to propose the wave nature of particles?

12.Explain the wave packet.

13. Show that the phase velocity can exceed the velocity of light in vacuum.

14. Explain the terms, ‘phase velocity’ and ‘group velocity’.

15. State and explain Heisenberg’s uncertainty principle.

16. Use uncertainty relation to show that the electron cannot stay in the nucleus.

17. Explain the terms operators and expectation value.

18. Why should a wave function obey the normalisation condition?

19. Write down the one dimensional time dependent Schrodinger wave equation and explain the meaning of each terms.

20. Derive the time dependent Schrodinger equation.

21. Derive the time independent Schrodinger equation.

22. Give comparative account of the energy of a free particle and a particle confined to one dimensional infinitely deep potential well.

23. Set up the Schrodinger equation for a particle in an infinite deep one dimensional potential well and find expression for the wave function and energy of the particle.

24. A particle is approaching a finite step potential with an energy greater than the height of the step. Set up the Schrodinger equation for the problem and derive expression for reflection and transmission coefficients.

25. Describe Davisson and German experiment on diffraction of electron and explain how it explains the nature of an electron beam.

26. State and explain the Heisenberg’s uncertainty principle with the suitable illustration.

27. Explain the physical signification of wave function.

28. Write Schrodinger equation for a particle in box. Solve it to obtain eigen values and eigen functions.

29. Derive time independent Schrodinger wave function for a nonrelativistic free particle. Explain significance of the wave function.

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