Answer to Question #134891 in Quantum Mechanics for Sarita

Question

In the ground state of harmonic oscillator,what is the probability of finding the particle outside the classical allowed region

Answer 1

$P_{classical}=\frac{1}{\sqrt\pi}\intop_{-1}^{1}e^{-\xi^2}d\xi$

This integral is the error function, so we find;

$P_{classical}=erf(1)=0.8427$

The probability of being outside the classical region is then;

$1-P_{classical}=0.1573$