Angular Momentum Operator in terms of ladder operators

[Plutoniummatt]

Homework Statement

http://img716.imageshack.us/i/captur2e.png/
http://img716.imageshack.us/i/captur2e.png/

Homework Equations

Stuck on the last part

The Attempt at a Solution

http://img689.imageshack.us/i/capturevz.png/
http://img689.imageshack.us/i/capturevz.png/

 

[Ben Niehoff]

You missed the

e^{\pm i \phi}

in the definition of L_{\pm}

 

[Plutoniummatt]

You missed the

e^{\pm i \phi}

in the definition of L_{\pm}

dont they multiply to give 1?

e^{ i \phi}e^{- i \phi} = 1

Edit:

you were right, i got it in the end taking into account the exponential factors...was a ***** of an algebra grindfest though