- #1

whatisreality

- 290

- 1

## Homework Statement

I think this is a square well potential problem. The question asks me to sketch the ground-state probability density, for the following situation:

A quasielectron moves in a 'quantum dot' device. The potential V(x) = 0 for 0 ≤ x < L, and is infinite otherwise.

## Homework Equations

## The Attempt at a Solution

I'm going to need to solve the Schrodinger equation within the device. I have no idea what a quantum dot is, but presumably it doesn't actually matter! I think you can just treat it like an infinite square potential. The Schrodinger equation is

##-\frac{\hbar^2}{2m} \frac{\partial \psi}{\partial x^2} = E \psi##

Within the device. And I also need boundary conditions. One of these boundary conditions is ##\psi(L)=0##, since the potential is infinite at L. Annoyingly, the potential is 0 at x=0, so I can't use the same reasoning there. So my first question is, how do I get my second boundary condition? I don't see how the potential being zero at x=0 in any way restricts what ##\psi## could be...