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Consider an arbitrary un-normalized wave function ψ expanded in terms of eigenstates of Hamiltonian H, where The correct option, which definitel
Question

Consider an arbitrary un-normalized wave function ψ expanded in terms of eigenstates of Hamiltonian H, where

The correct option, which definitely holds for any set of {an​}, is

A.

B.

C.

D.

Correct option is B

The variational method is one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states. This allows calculating approximate wavefunctions such as molecular orbitals.
The method consists of choosing a "trial wavefunction" depending on one or more parameters, and finding the values of these parameters for which the expectation value of the energy is the lowest possible. The wavefunction obtained by fixing the parameters to such values is then an approximation to the ground state wavefunction, and the expectation value of the energy in that state is an upper bound to the ground state energy.

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