Introduction to Quantum Mechanics · Problem 2.14

Time-Independent Schrödinger Equation — David J. Griffiths

Physics — Quantum Mechanics · harmonic_oscillator_classical_region

Problem

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? *Hint:* Classically, the energy of an oscillator is E=(1/2)ka2=(1/2)mω2a2E = (1/2)ka^2 = (1/2)m\omega^2 a^2, where aa is the amplitude. So the "classically allowed region" for an oscillator of energy EE extends from −2E/mω2-\sqrt{2E/m\omega^2} to +2E/mω2+\sqrt{2E/m\omega^2}. Look in a math table under "Normal Distribution" or "Error Function" for the numerical value of the integral, or evaluate it by computer.

Related theory

Browse the problem library