I Why do I get to a contradiction?

[Gjmdp]

I don't understand why LzL+ acting over m is Planck constant(m+1) L+|m>. I 've done it and I've got to a contradiction. Am I doing something wrong?

 

[DrClaude]

Your notaion is difficult to understand. Do you mean
$$
L_z L^+ | l,m \rangle = \hbar (m+1) L^+ | l,m \rangle
$$
with $L^+$ the raising operator and $| l,m \rangle$ an eigenstate of $L^2$ and $L_z$ (with quantum numbers $l$ and $m$)?

If so, what is the result of $L^+ | l,m \rangle$?

 

[Demystifier]

I've got to a contradiction. Am I doing something wrong?

Even though you didn't say what exactly have you done, the above is sufficient to conclude that the answer is - yes.

 

[Gjmdp]

Even though you didn't say what exactly have you done, the above is sufficient to conclude that the answer is - yes.

Yup that is very probable. But, there's still the option I didn't understand some of the mathematics, and yet, I may not have done anything wrong.

 

[Smalde]

Yup that is very probable. But, there's still the option I didn't understand some of the mathematics, and yet, I may not have done anything wrong.

Then please show us what you have already done.