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Subject: MATLAB modeling of finite quantum model
Date: Sat, 16 Aug 2008 03:22:02 +0000 (UTC)
Organization: McMaster University
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I am currently programming a model of a finite quantum well and have run 
into a couple of problems. After applying boundary conditions, I get two 
equations: 

tan(theta) = sqrt(theta_knot^2/theta^2 - 1)
cot(theta) = -sqrt(theta_knot^2/theta^2 -1)

The parameters theta and theta_knot have the width of well, barrier potential, 
and mass of the electron embedded in them. 

I tried solving this in two ways:

1) I arranged loops to solve using the "solve" command for transcendental
equation but the cotangent argument was causing a problem.

2) My other attempt consisted of incrementing theta between odd intervals of 
pi for tangent and even intervals of pi for cotangent until upon substitution 
into the above equations they did equal within 0.00000001. This approach is 
currently giving me some problems. Am on I doing this correctly or is there a 
better way. A friend suggested using Newton-Raphson method but I am 
unsure how to apply this because as far as I am aware that method is for 
finding zeroes and I am interested in the intersections of these equations so 
that I can derive the possible energy levels. Thanks in advance.

Nik