Question

Write down L- lowering operator

Answer 1

$$L_{-}=L_{x}-iL_{y}\\L_{-}=-i\hbar\left(y\frac{\partial }{\partial z}-z\frac{\partial }{\partial y}\right)-i(-i\hbar)\left(z\frac{\partial }{\partial x}-x\frac{\partial }{\partial z}\right)\\L_{-}=-i\hbar\left(y\frac{\partial }{\partial z}-z\frac{\partial }{\partial y}\right)-\hbar\left(z\frac{\partial }{\partial x}-x\frac{\partial }{\partial z}\right)$$