Problem 2.14 In the ground state of the harmonic oscillator, what is the probability (correctto 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) mo²a², where ais the amplitude. So the “classically allowed region" for an oscillator of energy E extendsfrom –/2E/mw² to +/2E/mo². Look in a math table under “Normal Distribution" or"Error Function" for the numerical value of the integral, or evaluate it by computer.

Understanding of this question is very easy because its just an small integral. But hardest point is…

Problem 2.14 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) mw²a², where a is the amplitude. So the “classically allowed region" for an oscillator of energy E extends from –/2E/mo² to +/2E/mo². Look in a math table under “Normal Distribution" or "Error Function" for the numerical value of the integral, or evaluate it by computer. -

Problem 2.14 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) mw²a², where a is the amplitude. So the “classically allowed region" for an oscillator of energy E extends from –/2E/mo² to +/2E/mo². Look in a math table under “Normal Distribution" or "Error Function" for the numerical value of the integral, or evaluate it by computer. -