Calculating Lowest Energy Levels of a Rigid Spherical/Cubic Box

[quantumdude10]

Homework Statement

Determine the four lowest energy levels, their degeneracies and quantum numbers of the wavefunctions for an electron in

i) a rigid spherical box of 2 Angstrom radius and,

ii) a rigid cubic box of the same volume

Express the result in multiples of ħ2/(2m0a2), and in electron Volt units. Plot the result on energy level diagrams and comment.

Homework Equations

Schroedinger's equation in spherical coordinates...

The Attempt at a Solution

Not sure how to solve 3d questions...

 

[Hootenanny]

Welcome to Physics Forums.

How about we start with writing out Schrödinger's equation with the laplacian in spherical coordinates.

Do you know what the usual ansatz is for 3D spherically symmetric problems?

 

[quantumdude10]

you mean this one?

is there a way to post those equations to the body directly and not as an attachment?

 

[G01]

you mean this one?

is there a way to post those equations to the body directly and not as an attachment?

You can use the $\LaTeX$ typsetting feature of the forum:

https://www.physicsforums.com/showthread.php?t=8997

 

[Hootenanny]

you mean this one?

That's the one. Now, do you know the appropriate ansatz?