- #1

Talib

- 7

- 0

Can anyone lead me or give me a hint on how to solve this problem?

Interaction between neutral atoms and molecules can be decomposed to

two different forces: an attractive force at large distances (the Van der

Waals force), and a repulsive force at short distances (due to overlap between electron wavefunctions). A simple mathematical description of this

interaction between two particles is given by the Lennard-Jones potential:

U (r) = 4*epsilon [(sigma/r)^12 - (sigma/r)^6]

where [sigma] and [epsilon] are empirical parameters (epsilon is the depth of the potential well and sigma is the (finite) distance at which the potential is zero), and r is the distance between the particles.

(a) Sketch this potential.

(b) Are there any forbidden regions? If so, what are they and why? If

not, why not?

(c) Obtain an estimate for the number of allowed energy levels corresponding

to bounded states.

(d) Calculate the energies of these (bounded) energy levels.

Thanks a lot! :D

Talib