If the wavefunction for $1$D PIB is Y $"()=$ #

$ $\%$ sin $"\%$&

$ $,$ how could we write a

separable wavefunction, Y $",=$ X $$ Y $,$ for $2$D PIB?

$$ If the energy for $1$D PIB is $"=\text{'}!"!$

$()$$$!,$ what is the total energy for the $2$D PIB?

$$ If the box is rectangular, L x$$Ly$,$ is the wavefunction still separable and does the

energy have the same form as for the square box?