Paper: CSIR-NET June 2013 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Quantum Chemistry – General · Marks: 2 · Difficulty: Medium
The wave function $\psi$ of a certain system is the linear combination $\psi=\sqrt{\frac{1}{4}} \psi_{1}+\sqrt{\frac{3}{4}} \psi_{2}$ where $\psi_{1}$ and $\psi_{2}$ are energy eigen functions with eigen values (non-degenerate) $\mathrm{E}_{1}$ and $\mathrm{E}_{2}$ respectively. What is the probability that the system energy will be observed to be $\mathrm{E}_{1}$ ?
(a)$\sqrt{\frac{3}{16}}$
(b)$\frac{3}{4}$
(c)$\frac{1}{4}$
(d)$\sqrt{\frac{1}{4}}$
Answer
Answer: B ✓ checked by 4AB · confidence medium
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
ψ = (√3/2)ψ₁ + (1/2)ψ₂: the probability of measuring E₁ is |c₁|² = 3/4.