Potential In the Wave Equation

Most recent answer: 01/17/2014

Q:
The time independent wave equation carries a term of kinetic energy plus potential energy. But the potential energy term is really just voltage potential. Energy is voltage potential times charge. Charge does not show up in the equation. How do the units of energy and voltage add up? Does the wave equation assume the particle have a charge? Doesn't the wave equation also apply to particles with no charge?
- Noel Delgado (age 41)
Oro valley, AZ, Us
A:

Hi Noel,

"But the potential energy term is really just voltage potential." Actually, the potential energy term in the Schrodinger equation can be any kind of potential energy (PE). For example, it could be gravitational PE (mgh), or as you say electrical PE (q*Φ, where Φ is the scalar potential).

The units of q*Φ are energy, so they can be added to the other energy terms in the wave equation. If the particle is charged, it will have this term; if it isn't, then set q = 0 and the term disappears as it should.

David Schmid


(published on 01/17/2014)