Addition of Angular Momenta in Quantum Mechanics

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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.
Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA
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Details
Reference: S. M. Blinder, Introduction to Quantum Mechanics, Amsterdam: Elsevier, 2004 pp. 85–86.
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"Addition of Angular Momenta in Quantum Mechanics"
http://demonstrations.wolfram.com/AdditionOfAngularMomentaInQuantumMechanics/
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Published: March 7 2011