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*Consider a box with length, width and height given by L. The box encompasses the region*

described by 0<=x<=L, 0<=y<=L, and 0<=z<=L. A scalar field inside the box satisfies the

differential equation:

Here a is a positive constant that is equal to 30/L2.

The field is 0 on the surfaces y=0, y=L, x=0, x=L and finally the surface z=L.

On the surface z=0, the field has the functional form:

Solve for ψ as a function of x, y, and z inside the box. Your final solution must be

an analytic expression, though it can involve an infinite sum.

described by 0<=x<=L, 0<=y<=L, and 0<=z<=L. A scalar field inside the box satisfies the

differential equation:

**∇^2 ψ = −aψ**Here a is a positive constant that is equal to 30/L2.

The field is 0 on the surfaces y=0, y=L, x=0, x=L and finally the surface z=L.

On the surface z=0, the field has the functional form:

**ψ(x, y) = ( 1-|x-2/L|*2/L)(1- |x-2/L|*2/L)**Solve for ψ as a function of x, y, and z inside the box. Your final solution must be

an analytic expression, though it can involve an infinite sum.

What I don't understand is that ψ is time-independant wave, correct? and if so, how do I solve this when the boundry on one face is clearly not a wave. Please point me in the right direction to figure out how to do this. thanks.