How to Proove that L+ = L1 + iL2

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To prove that L+ = L1 + iL2, one must start with the definitions of L1 and L2 in terms of spherical coordinates. The expression for L+ is given as L+ = ~he^iφ (∂/∂θ + i cotθ ∂/∂φ). Understanding the relationship between angular momentum operators in quantum mechanics is crucial for this proof. The discussion emphasizes the importance of showing the equivalence through mathematical manipulation of the operators involved. A clear step-by-step approach to the derivation is essential for successfully completing the proof.
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Homework Statement


Hello All,

The professor asked us to prove that L+ = L1 + iL2,

Please Help!, I have no Idea how to proceed,

Any insight will be highly appreciated.

Homework Equations


L+ = L1+iL2=~he^iφ (∂/∂θ + i cotθ ∂/∂φ)

The Attempt at a Solution

L+ = L1+iL2=~he^iφ (∂/∂θ + i cotθ ∂/∂φ)
.
 
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