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engstruggle
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Homework Statement
Spin Operator S has eigenvectors |R> and |L>,
S|R> = |R>
S|L> =-|L>
eigenvectors are orthonormal
Homework Equations
Operator A is Hermitian if <ψ|A|Θ> = <Θ|A|ψ>*
The Attempt at a Solution
<ψ|S|L> = <L|S|ψ>* // Has to be true if S is Hermitian
LHS: <ψ|S|L> = <ψ|-|L>
<ψ|-|L>* = <L|-|ψ>
Question: how do i know how S acts on any function like |ψ> ?
Could somebody provide an algorithm to find if an operator is Hermitian.
I have another example of operator P, where P|R> = |L>
P|L> = |R>
How should i go on about this?