Normalized function and minimum energy

[satach]

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

 

[dx]

Have you tried using the hint? What did you get after writing |ψ> in the energy basis?

 

[satach]

no, i didn't try , because i don't know how to start :D

 

[dx]

Do you know what an eingenstate is?

 

[satach]

in polish language is sometnihg like : expand |Ψ> in base of self functions of H ...