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So i've been working on some very basic QM mathematics. Basically I've worked out the wave equation for a particle in one dimension (briefly) like so:

The trouble I'm having is trying to extrapolate this to two spatial dimensions (if that can be done in the fashion I'm trying).Code (Text):

-[tex]\frac{\hbar [SUP]2[/SUP]}{2m}[/tex][tex]\psi[/tex]"(x) + V(x)[tex]\psi[/tex](x) = E[tex]\psi[/tex](x)

V = 0 for 0 < x < L ; (L = "Length" of the Boundary)

=> [tex]\psi[/tex](x) = A sin([tex]\frac{n \pi x}{L}[/tex])

=> A = [tex]\frac{L}{2}[/tex]

I follow the same process except my solution to the Schrodinger equation (solution to the differential equation) is

The problem is that instead of finding the 'constants' A and B i've now got a relationship between them.Code (Text):

[tex]\psi[/tex](x,y) = A sin([tex]\frac{n \pi x}{L}[/tex]) + B sin([tex]\frac{n \pi y}{L}[/tex])

A[SUP]2[/SUP]([tex]\frac{L}{2}[/tex])y + B[SUP]2[/SUP]([tex]\frac{L}{2}[/tex])x = 1

^ From Normalizing the Solution with Limits of integration for the double integral of 0 < (x,y) < L

If someone could point out what I did wrong in my process (determine the wave equation differential equation, normalize and solve) and if that's alright where I go from here in writing the full wave-function of the model, I'd greatly appreciate it.

Thanks!

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# Wave Equation in 2 Dimensions - Basic

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