what is a particle in a box?

Question

general solutions

Answer 1

The term "particle in a box" is the name of an elementary quantum mechanic model. It refers to the solution of Schrödingers equation for one particle (so you don't have to consider complicated many body effects) usually in a 1-dimensional potential well of infinite height. Under these circumstances Schrödinger's equation (which usually is a complicated differential equation) can be easily solved analytically, and you get a simple but exact solution from which you can see many many of the elementary principles of quantum mechanics, for example quantization of energy levels and Heisenberg's principle of uncertainty. So it's basically a toy model for your first course in quantum mechanics.

Current nanotechnologies allow to build similar systems in the real world, and a lot of applications use these devices, for example the HE MT (High Electron Mobility Transistors) you find in your mobile phone or in your satellite receiver.

Answer 2

The above two answers are correct. See the wikipedia source below for information about solving Schrödinger's wave equation for the particle in a box case. Wikipedia is really great for these kinds of questions. It always has the math.

Answer 3

A useful vehicle to illustrate wave functions. The wave function in a rectangular box has a reasonably straightforward solution, unlike real world applications, which usually can be solved only numerically by computer (if at all).