- #1

Caulfield

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## Homework Statement

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 = ∫0^1/2 x^2e^(-x2/2) dx is known and express your result as a function of α)

## Homework Equations

distance from 0 to d; d = (mk)^(-1/4) *√ħ/2

s=[km^(1/4) /ħ^2]*x

Normalize condition: Cn = 1/ (π^2√(2^nn!)

Harmonic Oscillator wave function for n = 1 ψ1 = C1(2s)e^-s2/2

## The Attempt at a Solution

Is the formula that I want to use here p=ψ∗(x)ψ(x) or

p=∫ψ∗(x)ψ(x)dx? (p stands for probability.)

s=[km^(1/4) /ħ^2]* (mk)^(-1/4) *√ħ/2 = 1/2

C1=1/π^2√2 so ψ1 = (1/π^2√2)e^-1/2

so, now, do I use:

p=ψ∗(x)ψ(x)= [(1/π^(2)√2)e^-1/2]^2= 1/2π^4 * e^-1

I believe that this is the right way, but the hint confuses me.