The following are the three statements about perturbation theory(A) Second order perturbation correction to the ground state energy is ALWAYS negative.(B) Sum of the zero${ }^{\text{th}}$ order and the first order corrections to the ground state energy is ALWAYS greater than the exact ground state energy.(C) Sum of the zero${ }^{\text{th}}$ order and first order corrections to the ground state energy is less than the exact state energy.From the following which one is correct?
(a)Only A is true
(b)Both A and B are true
(c)Only C is true
(d)Both B and C are true
Answer
Answer: B ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
The second-order correction to the ground state is a sum of negative terms, so it is always negative (A true); E⁽⁰⁾ + E⁽¹⁾ = ⟨ψ⁽⁰⁾|H|ψ⁽⁰⁾⟩ is a variational upper bound, so it is ≥ the exact energy (B true, C false).