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messier992

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## Homework Statement

I'm trying to reconcile the answers to two questions regarding the average potential and kinetic energies in simple harmonic oscillator

Question 1:

The average potential energy of the vibrational motion in the ground state of a

diatomic molecule is 12 meV. The average kinetic energy of the vibrational motion

in that state is:

Answer: 12meV?

Question 2:

The ground state energy of a particle in a harmonic oscillator potential is E. The average kinetic energy of that particle in that state is

## Homework Equations

Potential Energy = 1/2*k*x^2

Total Energy = Kinetic + Potential Energy

## The Attempt at a Solution

To find the ratio of potential to kinetic energy:

the total potential energy is given by the integral of x^2 from -1 to 1 => 2/3

the total kinetic energy is given by the integral of 1-x^2 from -1 to 1 => 4/3

Therefore, the average kinetic energy should be twice the average potential energy