Question

Using separation fo variables in Cartesian coordinates to solve the 3D particle in a box:

V(x, y, z) ∫ [infinity]⁰ x, y, z all between 0 and a; oo, otherwise.
(a) Find the wavefunctions of the time-independent energy eigenstates.

Answer 1

To solve the time-independent Schrödinger equation for a particle in a box and find the wavefunctions of the time-independent energy eigenstates, use separation of variables in Cartesian coordinates and ensure that the conditions of termination at the box wall, symmetry about x = 0, and normalizability are met.

Step-by-step explanation:

To solve the time-independent Schrödinger equation for a particle in a box, we need to use separation of variables in Cartesian coordinates.

The wave function must terminate at the box wall, be symmetric about x = 0, and be normalizable to ensure finitude of the probability density. By solving the equation, we can find the wavefunctions of the time-independent energy eigenstates.