# Quantum mechanics, vectorrepresentation

1. Jun 3, 2012

### Kentaxel

1. The problem statement, all variables and given/known data

For the function

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

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

2. Jun 3, 2012

### 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.

3. Jun 3, 2012

### Kentaxel

So what do i need to find them? I got the vectors from the Jy-matrix and its eigenvalues, could i use this somehow? I also know J+, J-, Jz 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.

4. Jun 3, 2012

### vela

Staff Emeritus
Solution to what?