- #1

Nezva

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**Calculate [L**

_{z},L_{+}]By defintion ladder operators are:

L

_{+}=L

_{x}+iL

_{y}

L

_{-}=L

_{x}-iL

_{y}

Important Relations:

L

_{x}L

_{y}= i[tex]\hbar[/tex]L

_{z}, L

_{y}L

_{z}= i[tex]\hbar[/tex]L

_{x}, L

_{z}L

_{x}= i[tex]\hbar[/tex]L

_{y}

L

_{x}= yp

_{z}- zp

_{y}, L

_{y}= xp

_{z}- zp

_{x}, L

_{z}= xp

_{y}- yp

_{x}

To start solving;

[L

_{z},L

_{+}]

L

_{z}- (L

_{x}+ iL

_{y}) = 0

Multiply through by [tex]\hbar[/tex]:

[tex]\hbar[/tex]L

_{z}- [tex]\hbar[/tex]L

_{x}+ i[tex]\hbar[/tex]L

_{y}

The i[tex]\hbar[/tex]L

_{y}is equal to L

_{z}L

_{x}. From this point

I've tried varying approaches in attempt to cancel variable out, but have failed. I have a feeling this problem can be solved easier. Should I try to use spherical coordinates instead of Cartesian? From trying to figure this out I have stumbled upon the answer but I would like to know how to produce the answer.

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