Calculating Electron Energy in a One-Dimensional Potential Well

[delrepublica]

[SOLVED] Energy in a Potential Well

I so need help with this!

"The width of a one-dimensional potential well of an electron can be assumed to be about 2 A (there's a weird-looking bubble on top of the A). Calculate the energy of an electron (in Joules and in eV) from this information for various values of n. Give the zero-point energy."

Ok, so i know that if it's a one-dimensional potential well, the walls have infinetely high potential barriers. In other words, V0 is equal to infinity.

Could someone please help me out on this?

 

[tiny-tim]

Hi delrepublica! Welcome to PF!

I've no idea how to do that problem …

but I just thought I'd say hello! …

and tell you that you can impress your friends and professors by producing your own "weird-looking bubble": if you type alt-capital-A, it prints Å.

 

[pam]

The \AA stands for the Swedish name of the physicist \AAngstrom,
which is how this practical atomic length unit is pronounced (if you can pronounce Swedish).
Not all quantum wells are infinite square wells, but if this one is, it should be fully worked out in your textbook.

 

[physixguru]

particle in a box (also known as the infinite potential well or the infinite square well) is a problem consisting a single particle inside of an infinitely deep potential well, from which it cannot escape, and which loses no energy when it collides with the walls of the box. In classical mechanics, the solution to the problem is trivial: The particle moves in a straight line, always at the same speed, until it reflects from a wall.

The problem becomes very interesting when one attempts a quantum-mechanical solution, since many fundamental quantum mechanical concepts need to be introduced in order to find the solution. Nevertheless, it remains a very simple and solvable problem. This article will only be concerned with the quantum mechanical solution.

The problem may be expressed in any number of dimensions, but the simplest problem is one dimensional, while the most useful solution is the particle in the three dimensional box. In one dimension this amounts to the particle existing on a line segment, with the "walls" being the endpoints of the segment.

In physical terms, the particle in a box is defined as a single point particle, enclosed in a box inside of which it experiences no force whatsoever, i.e. it is at zero potential energy. At the walls of the box, the potential rises to infinity, forming an impenetrable wall. Using this description in terms of potentials allows the Schrödinger equation to be used to determine the solution.

 

[delrepublica]

Thank you guys so much for your help!
And yes, the A is angstroms, which made everything sooo much easier!

All I needed to do to solve it was use the equation En = [(Dirac's constant)^2 * pi^2 * n^2] / [2m* L^2]

and for the zero-point energy you just use n=1, so easy enough =)