Question

Using the commutation relations for the operators of angular momentum ( J_{x, y, z} ), show the following two identities. [ J_{-} J_{+}=J^{2}-J_{z}left(J_{z}+1 ight) ] and [ J_{+} J_{-}=J^{2}-J_{z}left(J_{z}-1 ight) . ]

          Using the commutation relations for the operators of angular momentum ( J_{x, y, z} ), show the following two identities.
[
J_{-} J_{+}=J^{2}-J_{z}left(J_{z}+1
ight)
]
and
[
J_{+} J_{-}=J^{2}-J_{z}left(J_{z}-1
ight) .
]

Added by Foster J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Lucas Finney

05/09/2022

Step 1

Step 1: Recall the definitions of the ladder operators \( J_+ \) and \( J_- \): \[ J_+ = J_x + iJ_y \] \[ J_- = J_x - iJ_y \] Show more…

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Using the commutation relations for the operators of angular momentum Jx,y,z, show the following two identities. J−J+ = J2 − Jz(Jz + 1) and J+J− = J2 − Jz(Jz − 1).