Degenerate Energy States

n

x

1

n

y

1

The probability function

2

ψ

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

n

x

and

n

y

, and varies as

2

n

x

+

2

n

y

. The plot shows how the probability function

2

ψ

changes with different values of

n

x

and

n

y

. The total energy

E

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

n

x

and

n

y

can be chosen to give the same values of

E

o

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