Wave Physics and basics of quantum mechanics

a) What is the superposition principle of the wave? What is the duality? And in what situations one should expect one nature rather than the other one? (6pt)

b) What is the physical significance of Ψ(x,y,z,t)*Ψ(x,y,z,t), where Ψ(x,y,z,t) is the wave function of an electron at point (x,y,z) and time t? What is the Heisenberg’s uncertainty principle? (4pt)

c) Define the Fermi Energy EF . Using energy bands to define the conductors, intrinsic semiconductors, and insulators. And where is the E F for each type of the materials? (10pt)

Quantum mechanics a) Use ONE sentence to describe the relationship between the energy and momentum (wavenumber) for each of the following cases: free electrons, electrons in infinitely high potential well and electrons in the crystal. (3pt)

A 5g marble is constrained to roll inside a tube of length L = 2 cm. The tube is capped at both ends.

b) Modelling this case using one of the special cases in (a), determine the corresponding quantum parameters if the marble is initially given an energy of 1.00 mJ. (5pt)

c) Calculate the excitation energy required to promote the marble to the next available energy state. (3pt)

d) Based on the relationship between classical physics and quantum mechanics, comment on your results in (c) (2pt)

Multiple Choice:

1) Superconductors can be treated as a:

a). paramagnetic material.

b). ferromagnetic material.

c). diamagnetic material.

d). Who knows.

2) The light emission can be classified into spontaneous and stimulated emission.

In a stimulated emission, the incident photo and the emitted photo have:

a). The same energy.

b). The same direction.

c). The same polarization direction.

d). Who knows.

3) You are going to fabricate semiconductor lasers using both direct band gap and indirect band gap semiconductors: a). Lasers made of indirect bandgap semiconductor have a higher efficiency. b). Lasers made of direct bandgap semiconductor have a higher efficiency. c). Lasers would have the same efficiency. d). Who knows.

4) The absorption spectrum is quite important in optical study of material band structure, which of the following is directly related to the absorption spectrum?

a). ε 1 .

b). ε2 .

c). ε 2 / ε1 .

d). n.

5) The Pauli principle tells us that:

a). one energy state can have two electrons.

b). one electron can have two energy states.

c). one electron can have two states: spin up and spin down.

d). one energy state is either occupied by two electrons or empty.