Solving for DeltaX in a Quantum Well: Uncertainty Principle and Energy Analysis

[D__grant]

Homework Statement

-This is a problem on my practice final that I haven't been able to solve. Hoping someone out there can take a crack & clarify it for me.

Quantum wells are devices which can be used to trap electrons in semiconductors. If the electron is in the well it has a lower energy than if it is outside, so it tends to stay in the well. Suppose we have a quantum well which has a width of DeltaX and a depth of 1.0 eV , i.e. if the electron is in the well it has a potential energy of -1.0 eV and if it is outside it has a potential energy of 0 eV. Use the uncertainty principle to find the value of DeltaX for which total energy kinetic & potential of an electron in the well is zero.
Note: This is the smallest size well we can have because if deltaX is any smaller, the total energy of the electron in the well will be bigger than zero, and escape.

Homework Equations

1. E=KE+PE
2. Vo= -1 eV
3. Total Energy > 1/2m x (h/2piDeltaX)^2 - Vo

The Attempt at a Solution

I set the Total Energy=0 and attempted to solve for deltaX. My first solution was the the order of 10^-11 but I doubt I answered it correctly. Also, the mass of an electron was not given on the exam so I'm wondering if there's a different path to take. Thank you

 

[D__grant]

Anyone care to take a shot at this? I'm desperate for help & I'm not sure why no one's attempted it. I read the stickies & tried following the forum's conventions as best I could...

thank you all