WOLFRAM|DEMONSTRATIONS PROJECT

Schwinger's Oscillator Model for Angular Momentum

n

a

0

1

2

3

n

b

0

1

2

3

In an internal Atomic Energy Commission document published in 1952 [1], Julian Schwinger developed the quantum theory of angular momentum from the commutation relations for a pair of independent harmonic oscillators. This work has since been subsequently quoted many times [2, 3]. A simplified version of the derivation is given in the Details. This Demonstration shows the angular momentum states

j

,

m

derived from the quantum numbers

n

a

,

n

b

for a pair of harmonic oscillators, with

n

a

,

n

b

=0,1,2,…

.