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Nusc
07/21/08 2:45pm

Hello. Below is a do loop:
Do[
If[1 + 2 \[Alpha] > 0 && 2 \[Alpha] < 1 + 4 \[Beta] && \[Beta] >= 0,
Print[
"alpha=", \[Alpha], ",",
"beta=", \[Beta], ",",
"x=", x =
PowerExpand[(\[Pi] \[HBar] (1 + 2 \[Alpha]))/(\[Pi] /
2 Sqrt[-((\[HBar]^2 (-1 + 2 \[Alpha] - 4 \[Beta]) (3 +
2 \[Alpha] + 4 \[Beta]))/\[Tau]^2)] \[Tau])], ",",
"t=", t =
PowerExpand[\[Pi] /
2 Sqrt[-((\[HBar]^2 (-1 + 2 \[Alpha] - 4 \[Beta]) (3 +
2 \[Alpha] + 4 \[Beta]))/\[Tau]^2)]], ",",
"Eigenvalues=",
PowerExpand[{1/2 (-x \[Tau] - Sqrt[4 + (x)^2] \[Tau]),
1/2 (x \[Tau] - Sqrt[4 + (x)^2] \[Tau]),
1/2 (-x \[Tau] + Sqrt[4 + (x)^2] \[Tau]),
1/2 (x \[Tau] + Sqrt[4 + (x)^2] \[Tau])}], ",",
"New Hamiltonian=",
new = MatrixForm[{{0, -\[Tau], 0, 0}, {-\[Tau],
0, -PowerExpand[x] \[Tau], 0}, {0, -PowerExpand[x] \[Tau],
0, -\[Tau]}, {0, 0, -\[Tau], 0}} +
PowerExpand[{{1/2 (-x \[Tau] - Sqrt[4 + (x)^2] \[Tau]), 0, 0,
0}, {0, 1/2 (x \[Tau] - Sqrt[4 + (x)^2] \[Tau]), 0, 0}, {0,
0, 1/2 (-x \[Tau] + Sqrt[4 + (x)^2] \[Tau]), 0}, {0, 0, 0,
1/2 (x \[Tau] + Sqrt[4 + (x)^2] \[Tau])}}]], ",",
"\!\(\*SubscriptBox[\"\[Phi]\", \"1\"]\)=",
f41 = Normalize[{1, 1/2 (x + Sqrt[4 + x^2]),
1/2 (x + Sqrt[4 + x^2]), 1}], ",",
"\!\(\*SubscriptBox[\"\[Phi]\", \"2\"]\)=",
ff41 = Normalize[{-1, 1/2 (x - Sqrt[4 + x^2]),
1/2 (-x + Sqrt[4 + x^2]), 1}], ",",
"\!\(\*SubscriptBox[\"\[Phi]\", \"3\"]\)=",
fff41 = Normalize[{1, 1/2 (x - Sqrt[4 + x^2]),
1/2 (x - Sqrt[4 + x^2]), 1}], ",",
"\!\(\*SubscriptBox[\"\[Phi]\", \"4\"]\)=",
ffff41 =
Normalize[{-1, 1/2 (x + Sqrt[4 + x^2]), 1/2 ( -x - Sqrt[4 + x^2]),
1}], ",",
Eigenvectors[new]
]
], {\[Alpha], -20, 20}, {\[Beta], -20, 20}]

I'm trying to find the eigenvectors of the matrix but it gives me null. So I took the commands out of it and put them below - see file.

How do I assign variables within a loop without screwing things up?

Attachment: script.nb, URL: ,

Subject (listing for 'Eigenvectors')
Author Date Posted
Eigenvectors Nusc 07/21/08 2:45pm
Re: Eigenvectors Nusc 07/22/08 11:28am
Re: Eigenvectors yehuda ben-s... 07/23/08 10:35am
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