3.B.: Both a particle and a wave??!




Before you saw how classical motion could be described by a moving probability distribution (Click here to review).

Now observe the moving probability distribution associated with quantum motion of a particle bouncing between two walls.


  • Start and stop the animation by clicking the buttons under the graph.

  • Mass is measured in units of electron masses (9.11 X 10-31 kg). Energy is measured in units of the binding energy of an electron to a proton in the hydrogen atom (2.18 X 10-18 Joules).

  • When mass is near the electron mass (mass=1), you will see significant quantum effects for most of the allowed energy range. You will see the probability distribution spread and develop oscillations, which arise from the wave-like nature of quantum motion.

  • When mass is near the proton mass (mass=1836), you will start to see quantum effects when energy is less than about 100.

  • When mass is much greater than the proton mass, the probability distribution will move back and forth and without the spreading and oscillations characteristic of quantum motion.

  • Probability of finding the particle is plotted as a function ofdistance from the left wall at various times in the interactive animation.


    In quantum mechanics, the spread of the probability distribution arises from a fundamental principle of nature, the uncertainty principle. In classical mechanics, the spread is all due to experimental error.