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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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