Question: An electron in an infinite square well with L = 10 -12 m is moving at relativistic speed; hence, the momentum is not given by

An electron in an infinite square well with L = 10-12 m is moving at relativistic speed; hence, the momentum is not given by p = (2mE)1/2.

(a) Use the uncertainty principle to verify that the speed is relativistic.

(b) Derive an expression for the electron’s allowed energy levels and

(c) Compute E1.

(d) By what fraction does E1 computed in (c) differ from the nonrelativistic E1?

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