Degenerate Energy States

The probability function (ψ^2) is used to determine the energy of a system, which is based on the quantum numbers (Subscript[n, x]) and (Subscript[n, y]), and varies as ((Subscript[n, x])^2)+((Subscript[n, y])^2). The plot shows how the probability function (ψ^2) changes with different values of (Subscript[n, x]) and (Subscript[n, y]). The total energy E of the system is shown in the bottom-left corner. Different values of (Subscript[n, x]) and (Subscript[n, y]) can be chosen to give the same values of (Subscript[E, o]). When different sets of quantum numbers lead to the same energy state, the system is said to be degenerate.

THINGS TO TRY

MouseOver

DETAILS

Snapshots 1 and 2: two-fold degenerate states occur when different values of (Subscript[n, x]) and (Subscript[n, y]) produce the same energy level; in this case E = 10(Subscript[E, o])

Snapshots 3, 4 and 5: three-fold degenerate states occur when different values of (Subscript[n, x]) and (Subscript[n, y]) produce the same energy level; in this case E = 50(Subscript[E, o])

RELATED LINKS

Contributed by: Douglas Kellis (Boise State University)

© The Wolfram Demonstrations Project & Contributors   |   Terms of Use