The raising (J+) and lowering (J_) operators are defined by J+=JX+ iJy and J_ = JX- iJy.Read the following passage to answer the given questions based on it. Choose the correct options. (Marks: 1)What would be J+J-OPTIONS J2 - Jz2 + hJz J - Jz2 + hJz J2 - J + hJz J2 - Jz2 -hJz
Question
The raising (J+) and lowering (J_) operators are defined by J+=JX+ iJy and J_ = JX- iJy.Read the following passage to answer the given questions based on it. Choose the correct options. (Marks: 1)What would be J+J-OPTIONS J2 - Jz2 + hJz J - Jz2 + hJz J2 - J + hJz J2 - Jz2 -hJz
Solution
The correct option is J^2 - Jz^2 + hJz.
Here's the step by step calculation:
J+J- = (Jx + iJy)(Jx - iJy) = Jx^2 - i^2Jy^2 = Jx^2 + Jy^2 = J^2 - Jz^2 (since J^2 = Jx^2 + Jy^2 + Jz^2) = J^2 - Jz^2 + hJz (since the commutation relation [Jz, J±] = ±hJ±)
So, the correct answer is J^2 - Jz^2 + hJz.
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