I am having a devil of a time trying to successfully perform an iterative process for a particle’s energy in a finite well. The equation describing the energy for a finite well is transcendental thus requiring a graphical or numerical solution. Although, the graphical solution is straight forward I choose to pursue the numeric solution.(adsbygoogle = window.adsbygoogle || []).push({});

The only Internet resource I have been able to find that addresses the subject in specific detail is a page at the hyperphysics site:

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/pfbox.html#c1

(Page down about 4 pages to “Numerical Solution for Ground State”

The specific problem is that I am not able to determine how to calculate the initial alpha or ‘attenuation coefficient’ as he calls it. If you wish to tackle my example here are the numbers you can plug into the input boxes and it automatically calculates the rest of the values.

Well Length: .39E-9 m or .39 nm

Electron Mass: 9.1E-31 kg

Infinite well ground state for n=1: .396508E-18 J or 2.474808 eV

Potential Energy U: 1.025393E-17 or 64 eV

The first estimate of the attenuation coefficient is: .401643E11 m

This is the number I can not determine how it is calculated. When I used the formula for alpha provided in the section I do not come anywhere close to his first estimated value.

This next link, at the bottom, provides the energy levels for the first 4 levels of a finite well using the variables described above.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/pbox.html

Pursuing this example may be the easiest way to help; otherwise, if anyone has a good reference on numerical solutions for finite well energies and if it is in an electronic form I would much prefer to study that document and try to solve the problem myself. Otherwise, any and all help is greatly appreciated.

RON

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# Finite Well Iterative Process

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