The commutation relations among the angular momentum operators, Îx, Îy, Îz, and β, are distinctive and characteristic of all angular momentum systems. Define two new angular momentum operators as Î+ = Îx + iÎy Î_ = Îx – iÎy 2 (a) Write the operator product, ÎÎ_, in terms of 1² and Î₂. Note: 1² = Îx² + Îy² + +Î₂². (b) Evaluate the commutator, [[², Î+]. (L+ is shorthand for Îx ± ily.) (c) Evaluate the commutator, [ο‚α].
The commutation relations among the angular momentum operators, Îx, Îy, Îz, and β, are distinctive and characteristic of all angular momentum systems. Define two new angular momentum operators as Î+ = Îx + iÎy Î_ = Îx – iÎy 2 (a) Write the operator product, ÎÎ_, in terms of 1² and Î₂. Note: 1² = Îx² + Îy² + +Î₂². (b) Evaluate the commutator, [[², Î+]. (L+ is shorthand for Îx ± ily.) (c) Evaluate the commutator, [ο‚α].
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![The commutation relations among the angular momentum operators, Lx, Ly, Lz, and β,
are distinctive and characteristic of all angular momentum systems. Define two new angular
momentum operators as
: Îx + ily
Î_ = Îx – iÎy
-
Î+
2
(a) Write the operator product, ÎÎ_, in terms of β and Î₂. Note: β = Îx² + Îy² + Îz².
(b) Evaluate the commutator, [1²,1+].
(L+ is shorthand for Îx ± ily.)
(c) Evaluate the commutator, [L₂,L+].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b0563a1-d191-4439-9203-aacf88b8a280%2Fbab3f824-5e7d-411f-8a07-082fdd808779%2Fjtj343o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The commutation relations among the angular momentum operators, Lx, Ly, Lz, and β,
are distinctive and characteristic of all angular momentum systems. Define two new angular
momentum operators as
: Îx + ily
Î_ = Îx – iÎy
-
Î+
2
(a) Write the operator product, ÎÎ_, in terms of β and Î₂. Note: β = Îx² + Îy² + Îz².
(b) Evaluate the commutator, [1²,1+].
(L+ is shorthand for Îx ± ily.)
(c) Evaluate the commutator, [L₂,L+].
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