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Why no solution to 3 eqns. in 3 unk. ?

• To: mathgroup at smc.vnet.net
• Subject: [mg5037] Why no solution to 3 eqns. in 3 unk. ?
• From: "Christopher R. Carlen" <crobc at epix.net>
• Date: Sat, 19 Oct 1996 16:40:37 -0400
• Organization: epix.net
• Sender: owner-wri-mathgroup at wolfram.com

Recently I tried to solve this system:

 -a x   + b   + c y z == 0
 -a x z + b z - c y   == 0
  a     + b   - c     == 0

for the variables, {x, y, z} .

Well, Mathematica fails to give two of the solutions that I get by 
hand, which are:

 x = -1
 y = i
 z = i

OR

 x = -1
 y = -i
 z = -i

Mathematica does give the solution:

 x = (c - a)/a
 y = 0

which is a valid solution.  But why does it not give the other two 
solutions ?

Obviously, this system is odd, so if anyone can characterize it, or 
explain what this all means, I'd appreciate it.

This system arose in determining the constants of Schroedinger's 
equation, from basic quantum mechanics.  I have simplified the 
problem to a generic case that behaves in the same manner as the 
actual physical problem.

_____________________
Christopher R. Carlen
crobc at epix.net
carlenc at cs.moravian.edu