Normalized function and minimum energy

satach
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please prove this:

<Ψ|H\overline{^}|Ψ>\geqE0
function |Ψ> is normalized.

prompt: (expand function |Ψ> in the eigenbasis of H operator, count average and use ortonormality of the H base)

exercise 5.2.2 , p.163 , "principles of quantum mechanics" Shankar
 
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Have you tried using the hint? What did you get after writing |ψ> in the energy basis?
 
no, i didn't try , because i don't know how to start :D
 
Do you know what an eingenstate is?
 
in polish language is sometnihg like : expand |Ψ> in base of self functions of H ...
 
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