Waves on a Circle

img_lrg/red_black_wave.jpg not found

© CK-12 Foundation.

The quantum mechanical description of a particle is a mathematical function called a "wavefunction" related to the probability of finding the particle at any point in space. This function takes the form of a wave, hence the name wavefunction. If a particle is constrained to move in a circle, as it would be if it moves in a single, compactified dimension, the wave must oscillate some definite number of times around the circle as shown on the left side of the illustration above. The red line on the right side of the illustration does not correspond to a particle's wavefunction because it doubles over on itself as it goes around the circle rather than coming back to the same point. Each possible number of oscillations around the circle corresponds to a distinct, or quantized, value of energy that the particle can have. We will learn more about quantum wavefunctions and quantized energy in Unit 5. (Unit: 4)