Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
Start Practicing

Worksheet: The Quantum Harmonic Oscillator


A quantum harmonic oscillator makes a transition from the state to the state and emits a 450-nm photon. What is the oscillator’s frequency?

  • A Hz
  • B Hz
  • C Hz
  • D Hz
  • E Hz


Atoms in a crystal lattice vibrate in simple harmonic motion. What is the force constant of the lattice if a lattice atom makes a transition from the ground state to first excited state when it absorbs a 525-μm photon? Use a value of kg for the mass a lattice atom.


A particle with mass 0.0300 kg oscillates back-and-forth on a spring with frequency 4.00 Hz. At the spring’s equilibrium position, the particle has a speed of 0.600 m/s. If the particle is in a state of definite energy, find its energy quantum number.

  • A
  • B
  • C
  • D
  • E


A billiard ball of mass 0.200 kg bounces back and forth between the cushions of a 1.50 m long table. No energy is lost during the ball’s motion or during its collisions with the cushions.

If the ball is in its ground state, how many years does it take to move from one cushion to the other?

  • A
  • B
  • C
  • D
  • E

How much energy is required to excite the ball from its ground state to its first excited state?

  • A J
  • B J
  • C J
  • D J
  • E J


A quantum mechanical oscillator vibrates at a frequency of 250.0 THz. What is the least energetic radiation that it can emit?