To normalize the wave function for the ground state of a simple harmonic oscillator.

Question

Whether the energy gap for a system decreases, is constant, or increases as the initial quantum number for the transition increases can be determined by calculating the second derivative of the energy level expression with respect to the quantum number. Calculate the second derivative with respect to the quantum number of the energy level expression for a linear rotor, EJ = hBJ(J+1) and also for the harmonic oscillator, Ev = hυ\upsilonυ(v+1/2).

Answer 1

Question

Chapter 40, Problem 25P

(a)

To determine

To normalize the wave function for the ground state of a simple harmonic oscillator.

(b)

To determine

The probability of finding the oscillator in a narrow interval of −δ/2<x<δ/2.

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