Calculate the probability that a simple harmonic oscillator in its ground state will be found beyond the classical turning points.

In quantum mechanics, the simple harmonic oscillator (SHO) is described by a potential function V(x)=12mω2x2V(x) = \frac{1}{2} m \omega^2 x^2, where mm is the mass of the particle, ω\omega is the angular frequency, and xx is the position. The classical turning points, xclx_{\text{cl}}, are the positions where the kinetic energy of the particle is zero, meaning all the energy is stored as potential energy. The classical turning points are given ___ __________ ________ _________ ___ _________ ________ _______ ________.
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