the problem is as follows: in the ground state of the harmonic oscillator what is the probabilty of finding the particle outside the classically allowed region. where the classically allowed nrg is given by E=(1/2)m*omega^2*a^2 (where a is the amplitude).(adsbygoogle = window.adsbygoogle || []).push({});

were given that psi(x)=(m*omega/pi*h-bar)^(1/4)*(2^n*n!)^(-1/2)*H(zeta)*e^(-zeta^2/2)

where H(zeta) depends on n, but for this problem n=0

so i figured that if the probabilty of this from 0 to infinity (which is 1/2) then subtract the probability from 0 to the classical nrg, then the remainer should be the probablity of finding it outside the said classical region. right?

but that leads to the problem of finding the integral of e^(-a*x^2) from 0 to classical nrg... and this doesn't seem possible... is it?

cheers!

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# Harmonic oscillator outside classically allowed region

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