GRE Physics GR1777, Problem 013 Solution

GRE Physics GR 1777 Problem Solution

013. Quantum Mechanics (Infinity potential wall)


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 $latex m$ inside a one-dimensional box are
$latex E_n = \\frac{\\hbar^2 k^2}{2m}$.

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

$latex E_n = \\frac{\\hbar^2 k^2}{2m} = \\frac{\\hbar^2 \\pi^2 n^2}{2m a^2} $.

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




Leave a Reply

Your email address will not be published. Required fields are marked *