QUESTION 3: Abstract angular momentum operators: In this problem you may assume t commutation relations between the general angular momentum operators Ĵ, ĴÎy, Ĵz. Use whenev possible the orthonormality of normalised angular momentum eigenstate |j, m) and that α = αiĴy, J²|j,m) = ħ²j(j +1)|j,m) and Îz|j,m) = ħm|j,m) . (a) Express Ĵ+Ĵ_ in terms of №² and Ĵ2. (b) Using the result from (a) find the expectation value (j,m|Î+Î_|j,m). (This is the no squared of the state Î_|j,m).)
QUESTION 3: Abstract angular momentum operators: In this problem you may assume t commutation relations between the general angular momentum operators Ĵ, ĴÎy, Ĵz. Use whenev possible the orthonormality of normalised angular momentum eigenstate |j, m) and that α = αiĴy, J²|j,m) = ħ²j(j +1)|j,m) and Îz|j,m) = ħm|j,m) . (a) Express Ĵ+Ĵ_ in terms of №² and Ĵ2. (b) Using the result from (a) find the expectation value (j,m|Î+Î_|j,m). (This is the no squared of the state Î_|j,m).)
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Transcribed Image Text:QUESTION 3: Abstract angular momentum operators: In this problem you may assume t
commutation relations between the general angular momentum operators Ĵ, Ĵy, Ĵz. Use whenev
possible the orthonormality of normalised angular momentum eigenstate |j, m) and that
α = Îx±iĴy, Ĵ²|j,m) = ħ²j(j + 1)|j,m) and Ĵz|j,m)
(a) Express ĴĴ_ in terms of Ĵ² and Ĵ₂.
=
ħmlj, m).
(b) Using the result from (a) find the expectation value (j,m|εÎ_|j,m). (This is the nor
squared of the state Î_|j,m).)
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