Wolfram Demonstrations Project

The probability function

is used to determine the energy of a system, which is based on the quantum numbers

and

, and varies as

. The plot shows how the probability function

changes with different values of

and

. The total energy

of the system is shown in the bottom-left corner. Different values of

and

can be chosen to give the same values of

. When different sets of quantum numbers lead to the same energy state, the system is said to be degenerate.

Snapshots 1 and 2: two-fold degenerate states occur when different values of

and

produce the same energy level; in this case

Snapshots 3, 4 and 5: three-fold degenerate states occur when different values of

and

produce the same energy level; in this case

Contributed by: Douglas Kellis (Boise State University)

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Degenerate Energy States