For the n = 1 harmonic oscillator wave function, find the probability p that, in an experiment which measures position, the particle will be found within a distance d = (mk)-1/4√ħ/2 of the origin. (Hint: Assume that the value of the integral α = ∫01/2 x2e-x2/2 dx is known and express your result as a function of α)
distance from 0 to d; d = (mk)-1/4√ħ/2
Normalize condition: Cn = 1/ (π2√2nn!)
Harmonic Oscillator wave function for n = 1 ψ1 = C1(2s)e-s2/2
s = (km)1/4/ħ1/2 x
The Attempt at a Solution
I first plugged in s and normalized condition into the harmonic oscillator wave function.
ψ(s) = (km/π)1/42x/√2ħ e-√(km)x2/2ħ
I'm not sure if this is the right approach to tackling this problem.