Ibach Luth - Solid State 1.11 (QM model for Van der Waals' equation )

[DrPhysics]

Homework Statement

Ibach Luth Solid State 1-11

Relevant Equations

Quantum Mechanical model for VanDerWalls equation

Hi Everyone, can you guys please help me with the exercise attached?

I knot that according to the book, van der Waals interaction is “charge fluctuations in atoms due to zero point motion.”

This is correct once you understand that they are not talking about zero point motion of nuclear coordinates, but of electron behavior.

I'm trying to complete the answers, but I'm stucked. Thanks a lot.

 

[etotheipi]

To start to visualise what's going on, you have two protons ($+e$) separated by a distance $R$ and whose masses are so large compared to the two electrons ($-e$) that they can be assumed to remain stationary. The picture looks like:

The electrons are at $x_1$ and $x_2$ respectively relative to their corresponding protons; can you write down the total energy of the two oscillators? The energy of each oscillator will consist of the kinetic energy of the electron and the potential energy of the dipole. That will be $\mathscr{H}_1$.

Note that, in working out $\mathscr{H}_2$, the question assumes you're using Gaussian units.