In the ground state of the harmonic oscillator, what is the probability (correct to three significant digits) of finding the particle outside the classically allowed region? Classically, the energy of an oscillator is E = (1/2)ka² = (1/2) mω²a² , where a is the amplitude. So the “classically allowed region” for an oscillator of energy E extends from to Look in a math table under “Normal Distribution” or “ErrorFunction” for the numerical value of the integral, or evaluate it by computer.

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√2E/mw²