Question

The state of a harmonic oscillator is given as Ψ =$\frac{1}{ √3}$ 𝜓0 -$\frac{1}{ √6}$ 𝜓1+$\frac{1}{ √2}$ 𝜓2 , where 𝜓0, 𝜓1 and 𝜓2 are the normalized wave functions of ground, first excited, and second excited states, respectively. Which of the following statement(s) is/are true?

• A. A measurement of the energy of the system yields 𝐸=$\frac{1}{2}$ ℏ𝜔 with non-zero probability
• B. A measurement of the energy of the system yields 𝐸 =$\frac{5}{3}$ ℏ𝜔 with non-zero probability
• C. Expectation value of the energy of the system 〈𝐸〉 = $\frac{5}{3}$ ℏ𝜔
• D. Expectation value of the energy of the system 〈𝐸〉 = $\frac{7}{8}$ ℏ𝜔

Answer 1

Answer: (A), (C)

A measurement of the energy of the system yields 𝐸=$\frac{1}{2}$ ℏ𝜔 with non-zero probability

Answer 2

The correct options are: A and C