Undergrad Normalizing Constant 3D Infinite Well

[RaulTheUCSCSlug]

For time independent Schrödinger's equation in 3-D

Where E_nx,ny,nz=(n_x/L_x²+n_y/L_y²+n_z/L_z²)(π²ħ²/2m
and Ψ_nx,ny,nz=Asin(n_xπx/L_x)sin(n_yπy/L_y)sin(n_zπz/L_z)

How do I normalize A to get (2/L)^3/2?

I don't think I understand how to normalize constants.

 

[blue_leaf77]

A normalized state $\psi$ means that the total probability described by this state, $|\psi|^2$, is equal to unity.

 

[RaulTheUCSCSlug]

So when A is (2/L)^3/2 then |\psi|^2 is equal to one since the probability density must go to one?

So to solve for A one would just go through |\psi|^2 = 1 then solve for A?

 

[jtbell]

The integral of $|\psi^2|$ over all space (or equivalently, over the entire volume of the well, since $\psi$ must be zero outside the well) must equal 1 in order for $\psi$ to be normalized.

 

[blue_leaf77]

So to solve for A one would just go through |\psi|^2 = 1 then solve for A?

No, not that which must be equal to 1. Take a look at jtbell's comment above.

 

[RaulTheUCSCSlug]

Right. So the purpose is to have the probability of the whole function sum up to 1. Okay. I went to office hours and got things clarified thank you!