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[tex] f( \hat H ) | \Psi > =0 [/tex] where [tex] | \Psi > [/tex] is an 'Eigenvalue'

of the operator 'T' my question is if in this case the number

[tex] \hat T | \Psi > =E_{n} | \Psi > [/tex] satisfy [tex] f( E_{n}) =0 [/tex]

so the energies are precisely the roots of f(x).

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# Operator theory

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