- #1

- 23

- 0

Ok, so the allowed energy states for a particle in a box are

[tex]E_n = \frac{\hbar^2 \pi^2}{2 m L^2} n^2 [/tex].

This seems to mean, as you increase the length L, the particle's energy will tend towards zero. When L becomes very large, the particle will be essentially free, and according to the above equation will have an energy of E~0.

But the minimum energy of a free particle should be its rest-mass energy, E = mc^2, not zero. Also, the ground state (n = 0) energy of a particle in a box is

*inversely*proportional to mass, while the ground state energy of a free particle is directly proportional to its mass.

How do you reconcile these ideas from quantum mechanics and relativity?