Q92 · CSIR NET Chemistry, June 2016
Paper: CSIR NET June 2016 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Marks: 2 · Difficulty: Medium
A particle is in a state $\phi=\psi_{1}+3\psi_{2}$ where $\psi_{1}$ and $\psi_{2}$ are eigenfunctions of the Hamiltonian of the particle with eigenvalues $E_{1}$ and $E_{2}$, respectively. The average energy of the particle in the state $\phi$ is
(a)$(E_{1}+9E_{2})/10$
(b)$(E_{1}+3E_{2})$
(c)$(E_{1}+9E_{2})/14$
(d)$(E_{1}+3E_{2})/10$
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
ψ = ψ₁ + 3ψ₂ normalises to (ψ₁ + 3ψ₂)/√10, so ⟨E⟩ = (E₁ + 9E₂)/10.
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