I am taking my first semester of QM so excuse my question if it is way off mark, totally wrong, or very well known.(adsbygoogle = window.adsbygoogle || []).push({});

As I understand it, one of the postulates of QM are that states evolve unitarily, a consequence (but not THE defining feature) of unitary transformations is that they are invertible.

Consider some system in state ∑ α^{i}|Ψ_{i}> where |Ψ_{i}> are the eigenstates of some observable. Now if I measure my system, then after the measurement the state will be |Ψ_{i}> i.e. it will be entirely in that state in which I found it to be.

If I am correct, then we can represent this by the transformation (1/α^{i})P_{i}where P_{i}is the projection onto the ith eigenstate and (1/α^{i}) rescales it so that <Ψ|Ψ> = 1.

The problem is that projections arent unitary. In general they arent even invertable. So am I wrong about measurements violating unitarity? Is unitary transformations not a strict requirement?

Thanks

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# Does measurement violate unitarity?

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