Dear ACS Chemists, Sirs!

I am an amature physicist.

I often do computer simulation, or resolve Schroedinger eigenvalue equation using computer.

The problem is the Coulomb potential.

Its amplitude decreases inversely with the distance from a electric charge.

The trouble occurs when I choose a lattice system of which one lattice point coincides with the charge position.

Then the computer shows message that zero division error has occured.

How are the professionals who are doing computation about an actually reallistic atom or a reallistic molecule resolving this trouble in order to obtain a numerically reliable solution?

Sincerely

Pithecantropus Japonicus who, in a cave, is tinkering an abacus without knowing its meaning.

April 15, 2013

Mitsuru,

I can only ask questions since I haven't experienced this type of computer modeling before.

As I understand it, this is a Materials Science and Engineering question more than a physics question. Are you attempting to describe or predict temporal quantum mechanical behavior of a lattice system with the Schroedinger wave function? Is there a deviation from Vegard's law? What if you tried separating the temporal and the spacial parts of the equation(s), and fixed each variable to a constant? Then would you be able to avoid a zero division error and provide a reliable solution?

I hope my response is helpful.

Best Regards,

Deborah Fox Walsh