Infinite and Finite Square-Well Potentials

These exercises will examine the different facets of a single particle in an infinite square-well potential.  The manner in which we will solve of the infinite well problem provides a good introduction to how more complicated quantum mechanical problems may be approached.  This problem is fully solvable and the implications of the solutions are readily discovered.  You may be thinking that this problem may seem to be yet another idealized physics problem that we solve simply because we can and has no real application.  However, since the 1980's, the capability to confine an electron to motion in 1- and 2-dimensions has existed.  Many of the optical properties of such devices, called nanostructures, can be understood by applying the theory described here.

This is a little more realistic situation when compared to the infinite potential well case.  Often the finite potential well is used as a first approximation of an atom.  The electron associated with an atom can have both bound and unbound states.

Sections 1 & 2

    

Infinite Square Wells

Section 3

Finite Square Wells

Refer to Section 6-5 of Modern Physics by Bernstein, Fishbane and Gasiorowicz for a full theoretical development of the infinite square-well problem.

Refer to Section 8-5 of Modern Physics by Bernstein, Fishbane and Gasiorowicz for a discussion of bound states.

Refer to Section 14-6 of Modern Physics by Bernstein, Fishbane and Gasiorowicz for an introduction to nanostructures.

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