Define the eigenstates

These are the energy eigenvalues; [Graphics:../Images/index_gr_9.gif] is the mode number, [Graphics:../Images/index_gr_10.gif] is the size of the well, [Graphics:../Images/index_gr_11.gif] is the mass.

Let's put in some values for an electron in a well of atomic proportions

[Graphics:../Images/index_gr_12.gif]
[Graphics:../Images/index_gr_13.gif]
[Graphics:../Images/index_gr_14.gif]
[Graphics:../Images/index_gr_15.gif]

These are the corresponding eigenfunctions, including the time dependence specified by the Schrodinger equation.

[Graphics:../Images/index_gr_16.gif]

The probability density is the square of the absolute value of the wavefunction

[Graphics:../Images/index_gr_17.gif]


Converted by Mathematica      September 25, 2000