Answer
The energies of the higher energy states of the trapped electron are multiplied by $\frac{1}{4}$
Work Step by Step
We can write an expression for the energy of an electron in a potential well:
$E_n = (\frac{h^2}{8m~L^2})~n^2$
We can write an expression for the energy of an electron in a potential well if the width $L$ is doubled:
$E_n = \frac{h^2}{8m~(2L)^2}~n^2= \frac{1}{4}~\frac{h^2}{8m~L^2}~n^2$
The energies of the higher energy states of the trapped electron are multiplied by $\frac{1}{4}$
