Angular Momentum, calculating uncertainties

[dwyersfire]

Any help would be great! I'm just starting off with Quantum and am having trouble with this problem.

Homework Statement

Angular momentum eigenstates |l,m> satisfy the equality in the Heisenberg uncertainty relationship.

Calculate the uncertainties of Delta Lz and Delta Ly in an eigenstate |l,m> using raising and lowering operators.

 

[NuclearNut]

I'm never sure how to use latex code properly so I'll do my best to make everything as clear as possible.

The way to go about this, I'm pretty sure would be to write

(delta Lx)^2 = <Lx^2> - <Lx>^2

then express Lx in terms of the Ladder operators.

L+ = Lx + iLy

L- = Lx - iLy

so you get

Lx = ((L+) + (L-))/2

Ly = ((L+) - (L-))/2i

then you can substitute these into the first equation and perform the operations, keeping track of the order of operators, and using orthogonality to say that

<L1,m1|L2,m2> = (zero if L1 and m1 are not equal to L2 and M2 respectively) or 1 if they are equal.


hope that helps