# What is square of angular momentum?

## What is square of angular momentum?

In the case of angular momentum, the square of the angular momentum and one of the x, y, x components of angular momentum form such a set. Therefore the state of the particle can be characterized by the eigenvalues of the angular momentum squared and of one of the projections onto a fixed axis of the angular momentum.

**Does LZ commute with H?**

Angular momentum operator L commutes with the total energy Hamiltonian operator (H).

### Does LX and LZ commute?

therefore Lx and Ly do not commute. Using functions which are simply appropriate posi- tion space components, other components of angular momentum can be shown not to commute similarly.

**Is XP Hermitian?**

Yes, xp isn’t Hermitian. You use integration by parts to move the derivatives around and the x factor will block that.

## Are angular momentum operators Hermitian?

are also Hermitian. This is important, since only Hermitian operators can represent physical variables in quantum mechanics (see Sect. 4.6).

**Which is the square of the total angular momentum operator?**

This new operator is referred to as the square of the total angular momentum operator. The commutation properties of the components of L allow us to conclude that complete sets of functions can be found that are eigenfunctions of L 2 and of one, but not more than one, component of L .

### How is angular momentum expressed in spherical coordinates?

ANGULAR MOMENTUM IN SPHERICAL COORDINATES. B.3 Angular Momentum in Spherical Coordinates. The orbital angular momentum operator Z can be expressed in spherical coordinates as: L=RxP=(-ilir)rxV=(-ilir)rx [arar+;:-ae+rsinealpea ~ a] , or as 635 (B.23) (B.24) L = -ili (~ :e – si~e aalp).

**What’s the difference between angular momentum and spin?**

There is another type of angular momentum, called spin angular momentum (more often shortened to spin), represented by the spin operator S. Spin is often depicted as a particle literally spinning around an axis, but this is only a metaphor: spin is an intrinsic property of a particle, unrelated to any sort of motion in space.

## Can you measure the magnitude of the angular momentum vector?

Hence, the commutation relations ( 531 )- ( 533) and ( 537 ) imply that we can only simultaneously measure the magnitude squared of the angular momentum vector, , together with, at most, one of its Cartesian components. By convention, we shall always choose to measure the -component, .