Angular momentum operators

In summary, to obtain the angular momentum operators Lx and Ly in the basis of Y^±1_1(θ,φ) and Y^0_1(θ,φ) in the Lz representation, one can use the raising and lowering operators L+ and L-. The matrices for Lx and Ly can be calculated using the given terms for the n'n and n'th terms, respectively.
  • #1
stunner5000pt
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Homework Statement


Obtain the angular momentum operators [itex] L_{x} [/itex] and [itex] L_{y} [/itex] in the basis of functions [itex] Y^{\pm1}_{1}(\theta,phi}[/itex] and [tex] Y^{0}_{1}(\theta,phi}[/itex] in Lz representation2. The attempt at a solution
To calculate the matrices for the Lx and Ly operators, do i simply have to take the relevant spherical harmonics and apply Lx and Ly like this

To form the Lx the terms are given for n'n term of the matrix

[tex] (L_{x})_{n'n} = <\psi^{(n'-2)}_{1}|L_{x}|\psi^{(n-2)}_{1}>[/tex]

from this i can determine the terms of the Lx matrix
similarly for the Ly matrix?

am i correct? Thanks for any help.
 
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  • #2
It's easier to use the raising and lowering operators L+ and L-.
 

1. What is angular momentum in quantum mechanics?

Angular momentum is a physical quantity that describes the rotational motion of a particle or system of particles. In quantum mechanics, it is a fundamental property of particles that determines their behavior in the presence of a magnetic field.

2. What are angular momentum operators?

Angular momentum operators are mathematical operators that represent the angular momentum of a particle in quantum mechanics. They are used to describe the relationship between the angular momentum of a particle and its position and momentum.

3. How do angular momentum operators act on quantum states?

Angular momentum operators act on quantum states by rotating them in space, similar to how a physical object rotates in space. The amount of rotation is determined by the value of the angular momentum operator.

4. What are the properties of angular momentum operators?

There are several properties of angular momentum operators, including the fact that they are Hermitian, meaning their adjoint is equal to themselves. They also have quantized eigenvalues, which means they can only take on certain values determined by Planck's constant.

5. How do angular momentum operators relate to the Uncertainty Principle?

Angular momentum operators play a role in the Uncertainty Principle, which states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This is because the angular momentum operators for position and momentum do not commute, meaning they cannot be measured simultaneously with complete accuracy.

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