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MathGroup Archive 2004

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Help with a calculation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51601] Help with a calculation
  • From: ss54 at york.ac.uk (Simone Severini)
  • Date: Wed, 27 Oct 2004 01:54:03 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Dear All,

I' m here asking for some help with the following calculation:

$\sum_{r=0}^{3}\operatorname{Re}\left(  \left(  \alpha_{3,r}^{\ast}%
-\alpha_{4,r}^{\ast}\right)  \left(  \alpha_{2,r}e^{-i\phi_{r}}-\alpha
_{1,r}e^{i\phi_{r}}\right)  \right)  =2\sqrt{2}$

$\sum_{r=0}^{3}\alpha_{j,r}\alpha_{k,r}^{\ast}=\delta_{j,k}$ with
$j,k=1,2,3,4$

$\sum_{j=1}^{4}\left\vert \alpha_{j,r}\right\vert ^{2}=1$ for $r=0,1,2,3$

Is Mathematica able to find solutions?

In case of affirmative answer, how do I program Mathematica for this task?

Apologies, in the case my question is in some way naive.

Thanks,
Simone


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