1. The Hilbert space

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The quantum system is represented in a two-dimensional complex Hilbert space, which we realize as $\Cset^2$ - the set of all column vectors

$\begin{displaymath} a=\pmatrix{ a_1 \cr a_2} \end{displaymath}$

(1)

where

and

are complex numbers, and with scalar product

defined by

$\begin{displaymath} (a,b)={\bar a}_1 b_1+{\bar a}_2 b_2 \end{displaymath}$

(2)

where the bar ${\bar c}$ stands for the complex conjugation of the complex number

2002-04-11