Suppose, the ground stationary state of a harmonic oscillator with force constant 'k' is given by $\psi_{0}=\exp \left[-\mathrm{Ax}^{2}\right]$ Then, A should depend on K as
(a)$\mathrm{A} \propto \mathrm{k}^{-1 / 2}$
(b)$\mathrm{A} \propto \mathrm{k}$
(c)$\mathrm{A} \propto \mathrm{k}^{1 / 2}$
(d)$\mathrm{A} \propto \mathrm{k}^{1 / 3}$
Answer
Answer: A ✓ checked by 4AB · confidence medium
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
ψ₀ = exp(−√(mk) x²/2ħ), so A = √(mk)/2ħ ∝ k^{1/2}.