(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle in the harmonic oscillator potential is in the first excited state. What is the probability of finding this particle in the classically forbidden region?

2. Relevant equations

probability of finding particle = integral of abs[psi squared] [a,b]

3. The attempt at a solution

So, I'm using mathematica to find the intersection point of my x probability distribution with the oscillator potential function.

Solve[ ((m*w)/(\[Pi]*h))^(1/4)*(2*m*w/h)^(1/2)*

Exp[-((m*w)/(2*h))*x^2] - (1/2) (w^2)*m*x == 0, x]

but I get the answer

{{x -> -(Sqrt[h] Sqrt[

ProductLog[(8 Sqrt[(m w)/h])/(h^2 Sqrt[\[Pi]] w^2)]])/(

Sqrt[m] Sqrt[w])}, {x -> (

Sqrt[h] Sqrt[

ProductLog[(8 Sqrt[(m w)/h])/(h^2 Sqrt[\[Pi]] w^2)]])/(

Sqrt[m] Sqrt[w])}}

and then when I use this in my integral I get the answer

1/Sqrt[\[Pi]]2 ((m w)/h)^(3/2) If[Re[1/h] Re[m w] > 0

which obviously isn't a number as expected and seems to contain imaginary numbers. I don't understand what I'm doing wrong but this problem doesn't seem like it should be so complicated.

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# Homework Help: Probability for finding particle outside potential well

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