- #1

- 464

- 0

## Homework Statement

I have a 2D square well with sides a.

What is the minimum momentum and energy for this well?

## Homework Equations

Minimum momentum given by Δp≈ℏΔx and Δp≈ℏΔy

Minimum energy given by ΔE≈ℏΔt

This might be right. It says to consider the Schrödinger Equation in 2D. I've never seen this in 2D, so I don't know if this is correct.

[tex]\frac{- \hbar^{2}}{2m} \left( \frac {\partial ^{2}}{\partial x^{2}} + \frac {\partial ^{2}}{\partial y^{2}} \right) \Psi (x,y,t) + U(x,y,t) \Psi (x,y,t) = i \hbar \frac{\partial}{\partial t} \Psi (x,y,t)[/tex]

## The Attempt at a Solution

So I first though I would separate the variables into a spatial piece and a time dependent piece and then relate those to the uncertainty principles above. But then realized that might not work since I am in 2D. Then again....can I split it into two spatial (one for x and one for y) set each of those in the uncertainty principle since they aren't axis dependent and then do the same for time.

Although I don't think that is right either since that doesn't give me a Δx,y,t.

Basically I am stuck at the beginning it seems.