- #1

- 1

- 0

**Homework Statement**

a) Determine the ratio (E

_{m}/E

_{n}) between two energy states of a particle in a one dimensional box of length l.

b) Show that this is consistent with the non-relativistic low-energy limit.

The attempt at a solution

The attempt at a solution

I have figured out a) using the de broglie wave-particle duality and the energy momentum relationship to get:

E

_{m}/E

_{n}= m

^{2}/n

^{2}but I am unsure what this non-relativistic low-energy limit is.

I though about using classical kinetic energy to (ie. non-relativistic) of the particle and using similar equations (de broglie wavelength, standing wave) but I realized using the assumption of a De Broglie wavelength implies its accordance with relativity and I find myself somewhat lost.