GRE Physics GR 1777, Problem 013 Solution

GRE Physics GR 1777 Problem Solution

013. Quantum Mechanics (Infinity potential wall)

Solution

Infinity potential wall problem is one of the basic problems in quantum mechanics. So I recommend you to remember some equation about it.

The energy eigenvalues of a particle of mass m inside a one-dimensional box are
E_n = \frac{\hbar^2 k^2}{2m}.

And the boundary condition (u(a) = 0) implies that
kL = n\pi where n = 1,2,3, ..

Thus,
E_n = \frac{\hbar^2 k^2}{2m} = \frac{\hbar^2 \pi^2 n^2}{2m a^2} .

In the ground state (n=1), it becomes
E_1 = \frac{\hbar^2 \pi^2}{2m a^2}.

Answer

(D)

Reference

https://en.wikipedia.org/wiki/Particle_in_a_box

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