A particle in a one dimensional harmonic oscillator in x-direction is perturbed by a potential $\lambda \mathrm{x}(\lambda$ is number). The first-order correction to the energy of the ground state
(a)is zero
(b)is negative
(c)is positive
(d)may be negative or positive but not zero
Answer
Answer: A ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
E⁽¹⁾ = λ⟨0|x|0⟩ = 0 since the ground state is even and x is odd.