(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use separation of variables in cartesian coordinates to solve the infinite cubical well (or "particle in a box"):

[tex]V(x,y,z) = \{^{0, if x, y, z are all between 0 and a;}_{\infty , otherwise.}[/tex]

2. Relevant equations

Well, I've been trying to use

[tex]\frac{1}{2}mv^{2} + V = \frac{1}{2m}(P^{2}_{x} + P^{2}_{y} + P^{2}_{z}) + V = E\Psi[/tex]

3. The attempt at a solution

[tex]\frac{1}{2}mv^{2} + V = \frac{1}{2m}(P^{2}_{x} + P^{2}_{y} + P^{2}_{z}) + V = E\Psi[/tex]

[tex]\frac{1}{2m}(P^{2}_{x} + P^{2}_{y} + P^{2}_{z}) + V = \frac{-\hbar^{2}}{2m}\frac{\partial^{2}}{\partial x^{2}} + V_{x} + \frac{-\hbar^{2}}{2m}\frac{\partial^{2}}{\partial y^{2}} + V_{y} + \frac{-\hbar^{2}}{2m}\frac{\partial^{2}}{\partial z^{2}} + V_{z}[/tex]

[tex]\hat{H}_{x} = \frac{-\hbar^{2}}{2m}\frac{\partial^{2}}{\partial x^{2}} + V_{x}[/tex]

[tex]\hat{H}_{y} = \frac{-\hbar^{2}}{2m}\frac{\partial^{2}}{\partial y^{2}} + V_{y}[/tex]

[tex]\hat{H}_{z} = \frac{-\hbar^{2}}{2m}\frac{\partial^{2}}{\partial z^{2}} + V_{z}[/tex]

[tex]\Psi = X(x)Y(y)Z(z)[/tex]

[tex](\hat{H}_{x} + \hat{H}_{y} + \hat{H}_{z})(X(x)Y(y)Z(z)) = E*(X(x)Y(y)Z(z))[/tex]

So getting it here doesn't really tell me what the energies are. Can I cancel out [tex]\Psi[/tex]?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Infinite Cubical Well in Cartesian Coordinates

**Physics Forums | Science Articles, Homework Help, Discussion**