Let's take a spin 1/2 system, and the trivial operator : [tex]A=\mathbb{I}=\left(\begin{array}{cc} 1 & 0\\0 & 1\end{array}\right)[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

Suppose X=(1,0) is the initial state before the measurement. Question :

A) Is the final state Y=X, for obvious reasons.

B)The eigenspace for the eigenvalue 1 of A is the whole R^2. A particular normalized eigenvector is parametrized by a polar angle and given by : [tex] Y=(\cos(\phi),\sin(\phi)) [/tex]. Y is the endstate of this particular measurement, and [tex] p(Endstate=Y)=|\langle X|Y\rangle|^2=\cos(\phi)^2[/tex].

Is A or B the correct answer ?

Remarks :

1) A is a particular case of B

2) How do you interprete [tex]\phi [/tex] physically in the context of quantum-mechanics ?

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# Non disturbing (?) measurement

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