Quantum mechanics, vectorrepresentation

[Kentaxel]

Homework Statement

For the function

\chi^{(y)}=c_{1}<br /> <br /> \left( \begin{array}{ccc}<br /> -1\\<br /> i\sqrt{2}\\<br /> 1\end{array} \right)<br /> +<br /> <br /> c_{2}<br /> <br /> \left( \begin{array}{ccc}<br /> 1\\<br /> 0\\<br /> 1\end{array} \right)<br /> +<br /> c_{3}<br /> <br /> \left( \begin{array}{ccc}<br /> -1\\<br /> -i\sqrt{2}\\<br /> 1\end{array} \right)<br />

how would i go on about finding the constants, is this enough information or is something missing?

 

[dextercioby]

The only condition on the vector is to be normalized. This won't provide you with nothing but a condition involving all 3 constants altogether. There is an infinite number of solutions.

 

[Kentaxel]

So what do i need to find them? I got the vectors from the J_y-matrix and its eigenvalues, could i use this somehow? I also know J₊, J_-, J_z and the eigenvectors/values for the (chi)z, could this be usefull? I can't figure out how to put it together but the full solution requires a normalized vector.

 

[vela]

Solution to what?