Question

If you double the amplitude, what happens to the frequency in a classical (non quantum) harmonic oscillator? In a quantum harmonic oscillator?

Short answer

Frequency will remain unchanged in case of classical (non quantum) harmonic oscillator, as well as in case of harmonic oscillator on doubling the amplitude.

Step-by-step solution

Concept Introduction

The mathematical relation between frequency, speed and wavelength is given by, $\mathrm{f}=\frac{\mathrm{c}}{\mathrm{\lambda }}$

Here$\mathrm{f}$ is the frequency,$\mathrm{c}$ is the speed of the light, $\mathrm{\lambda }$is the wavelength.

The value of $\mathrm{c}$in vacuum is$3.0\times {10}^8\mathrm{m}/\mathrm{s}$ .

The amplitude is defined as the displacement of the vibrating article up to its maximum extent from its original position (central position).

Dependency of the frequency in case of the classical harmonic oscillator as well as quantum harmonic oscillator

In case of classical (non quantum) harmonic oscillator, frequency is independent of the amplitude. So, on doubling the amplitude, frequency will remain unchanged.

In case of quantum harmonic oscillator, frequency is independent of the amplitude. So, on doubling the amplitude, frequency will remain unchanged.