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Subject: Re: MATLAB modeling of finite quantum model
Date: Sat, 16 Aug 2008 19:07:02 +0000 (UTC)
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"Nikolaus Jewell" <nik.jewell@gmail.com> wrote in message <g85h4q$1bs
$1@fred.mathworks.com>...
> ......
> tan(theta) = sqrt(theta_knot^2/theta^2 - 1)
> cot(theta) = -sqrt(theta_knot^2/theta^2 -1)
> .......

  If you are looking for real solutions and if 'sqrt' is considered non-negative, 
there are no solutions to your two equations!  You have only to multiply the 
left and right sides of the equations and get the impossible equality

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

to see that.

  If you permit one of the above square roots to be negative, you have

 1 = theta_knot^2/theta^2 - 1,

which leads to

 tan(theta) = + or - sqrt(1) = +1 or -1.

Hence theta = pi/4, 3*pi/4, 5*pi/4, or 7*pi/4.  Also

 theta_knot = + or - theta*sqrt(2)

  I would suggest you look more carefully into whatever analysis went into 
these original two equations of yours and see if some unwarranted 
assumptions were made.

Roger Stafford