Recall: The mass of a proton is approximately 1.67×10⁻²⁷ kg.

The energy levels of a quantum harmonic oscillator are given by the formula:

E_n=(n - 1/2)hf

where:

E_n is the energy of the n^th level,
n is the quantum number (0 for the ground state, 1 for the first excited state, etc.),
h is Planck's constant,
f is the frequency of the oscillator.

The frequency f of the oscillator can be calculated from the spring constant k and the mass m of the particle using the formula for the frequency of a classical harmonic oscillator:

Now, we can calculate the energy levels. Remember that the quantum number n starts at 0 for the ground state, so the first three energy levels correspond to n=0, n=1, and n=2.

0.00985519220848 = 9.9 meV

0.0295655560285 = 30 meV

0.04927546796 = 49 meV

A particle executes simple harmonic motion with an amplitude of 25 cm. As the particle passes through the equilibrium point, its speed is 5 cm/s. Calculate the maximum acceleration of the particle.