# Angular Momentum, calculating uncertainties

#### dwyersfire

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

1. The problem statement, all variables and given/known data

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.

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#### NuclearNut

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

(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

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