The eigenstates of the 1² and 1₂ operators can be written in Dirac notation as Ij m) where L²|j m) = j(j + 1)ħ²|j m) and_Î₂|jm) = mħ|j m). Using these relationships, and assuming that all angular momentum is evaluated in units of ħ (so you can set ħ = 1), evaluate the following operations for the state |j m) = 15,2). (b) (β — ħ²)² \j m) = (î² − 1)² |j m) 2 (a) (Îx² + ΂² − Î₂²) |j m)
The eigenstates of the 1² and 1₂ operators can be written in Dirac notation as Ij m) where L²|j m) = j(j + 1)ħ²|j m) and_Î₂|jm) = mħ|j m). Using these relationships, and assuming that all angular momentum is evaluated in units of ħ (so you can set ħ = 1), evaluate the following operations for the state |j m) = 15,2). (b) (β — ħ²)² \j m) = (î² − 1)² |j m) 2 (a) (Îx² + ΂² − Î₂²) |j m)
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Transcribed Image Text:The eigenstates of the 1² and Î₂ operators can be written in Dirac notation as Ij m) where
β|j m) = j(j + 1)ħ²|j m) and Î₂|j m) = mħ|j m).
Using these relationships, and assuming that all angular momentum is evaluated in units of
ħ (so you can set ħ = 1), evaluate the following operations for the state |j m) = 15,2).
(b) (β — ħ²)² \j m) = ([² − 1)² |j m)
2
2
2
(a) (Îx² + ΂² − Î₂²) |j m)
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