The correct statement about both the average value of position x and momentum p of a 1-d harmonic oscillator… · ABC26PH1268

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Harmonic Oscillator · Exam: CSIR NET JUNE 2014 · Marks: 2 · Difficulty: Medium

The correct statement about both the average value of position x and momentum p of a $1-\mathrm{d}$ harmonic oscillator wave function is

(a)$\langle\mathrm{x}\rangle \neq 0$ and $\langle\mathrm{p}\rangle \neq 0$

(b)$\mathrm{x}=0$ and $\mathrm{p} \neq 0$

(c)$\mathrm{x}=0$ and $\mathrm{p}=0$

(d)$\mathrm{x} \neq 0$ and $\mathrm{p}=0$

Answer

Answer: C ✓ checked by 4AB · confidence high

The source book printed no answer; this one was worked out and checked — see the explanation.

Explanation

Every harmonic-oscillator eigenfunction is symmetric about x = 0 and stationary, so ⟨x⟩ = 0 and ⟨p⟩ = 0.

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