Angular momentum in quantum mechanics is a quantized vector with magnitude

and component

in any direction, conventionally chosen as the

axis. The quantum numbers are restricted to integer or half-integer values:

, with

. Vector addition of two angular momenta

is restricted by a triangle inequality

with

. Although quantum formalism is indifferent to such interpretations, the addition of angular momentum in the absence of any electric or magnetic field can be pictured by a vector model in which

and

precess about

, which itself precesses about a

axis. The amplitude for addition of

and

to give

with component

can be expressed in terms of Clebsch–Gordan coefficients as

with the sum restricted by

. You can set the precessions into motion with the trigger control. To choose a new set of

and

values, pause and reset the trigger.