I think I'm trying to reconcile quantum mechanics and special relativity . . . or whatever I'm doing I'm pretty confused.(adsbygoogle = window.adsbygoogle || []).push({});

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 isinverselyproportional 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?

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# Energies of a particle in a box vs. free particle?

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