The commutation relations among the angular momentum operators, Lx, Ly, Lz, and L?, are distinctive and characteristic of all angular momentum systems. Define two new angular momentum operators as Î4 = Lx + iLy L_ = Lx – iLy (a) Write the operator product, L,L_, in terms of 1? and L2. Note: L² = L»´+ L,“ + L,´. (b) Evaluate the commutator, [L², L+]. (L4 is shorthand for L, = Lx ± iLy.) (c) Evaluate the commutator, [L2,L+].
The commutation relations among the angular momentum operators, Lx, Ly, Lz, and L?, are distinctive and characteristic of all angular momentum systems. Define two new angular momentum operators as Î4 = Lx + iLy L_ = Lx – iLy (a) Write the operator product, L,L_, in terms of 1? and L2. Note: L² = L»´+ L,“ + L,´. (b) Evaluate the commutator, [L², L+]. (L4 is shorthand for L, = Lx ± iLy.) (c) Evaluate the commutator, [L2,L+].
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![2. The commutation relations among the angular momentum operators, Lx, Ly, Lz, and L², are
distinctive and characteristic of all angular momentum systems. Define two new angular
momentum operators as
Î, = Lx + iLy
L_ = Lx – iLy
2
2
(a) Write the operator product, L„L_, in terms of L² and Lz. Note: L² = ΄² + ΄² + ΂“.
(b) Evaluate the commutator, [L²,L+].
(L4 is shorthand for L, = Lx ± iLy.)
(c) Evaluate the commutator, [L, L+].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fa6eb9a-87be-419d-aa10-5eb2dc2185a7%2F8d3e009b-95da-47c4-8575-6dde35838fb3%2F2f3vmba_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. The commutation relations among the angular momentum operators, Lx, Ly, Lz, and L², are
distinctive and characteristic of all angular momentum systems. Define two new angular
momentum operators as
Î, = Lx + iLy
L_ = Lx – iLy
2
2
(a) Write the operator product, L„L_, in terms of L² and Lz. Note: L² = ΄² + ΄² + ΂“.
(b) Evaluate the commutator, [L²,L+].
(L4 is shorthand for L, = Lx ± iLy.)
(c) Evaluate the commutator, [L, L+].
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