Contents

- 1 Does angular momentum operator commute with Hamiltonian?
- 2 Do the angular momentum operators commute?
- 3 What is a commutator in a motor?
- 4 What is the importance of angular momentum in atomic and molecular physics?
- 5 Why is the commutator of angular momentum zero?
- 6 Which is an example of commutation of Hamiltonian with momentum?

## Does angular momentum operator commute with Hamiltonian?

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

## Do the angular momentum operators commute?

The operator nature of the components promise difficulty, because unlike their classical analogs which are scalars, the angular momentum operators do not commute.

**What does it mean to commute with Hamiltonian?**

Operators or observables that commute with the Hamiltonian of the system are conserved quantities, e.g. angular momentum or spin. This means that these quantities do not change with time. Those that do not commute with the Hamiltonian, are not conserved quantities.

### Does momentum commute with angular momentum?

The total angular momentum of a particle is spin plus orbital angular momentum. The orbital component doesn’t commute with momentum, but the spin component does.

### Can you simultaneously know the momentum and angular momentum in the same direction?

So unless the commutator between two operators is zero, you can never observe both quantities at the same time.

**Does spin commute with angular momentum?**

Spin operators do have the same commutation relations as the angular momentum operators.

## What is a commutator in a motor?

The commutator assures that the current from the generator always flows in one direction. On DC and most AC motors the purpose of the commutator is to insure that the current flowing through the rotor windings is always in the same direction, and the proper coil on the rotor is energized in respect to the field coils.

## What is the importance of angular momentum in atomic and molecular physics?

Angular momentum plays a similar role in determining the symmetries and number of orbitals of each symmetry species in the molecular case. In an atom all of the angular momentum is electronic in origin.

**What is Hamiltonian physical significance?**

The Hamiltonian of a system specifies its total energy—i.e., the sum of its kinetic energy (that of motion) and its potential energy (that of position)—in terms of the Lagrangian functionderived in earlier studies of dynamics and of the position and momentum of each of the particles.

### Do commuting operators have the same eigenvalues?

Commuting Operators Have the Same Eigenvectors, but not Eigenvalues.

### Do components of angular momentum can be find out simultaneously?

The three components of the angular momentum cannot simultaneously have definite values except in the case where all three components simultaneously vanish. Angular momentum is fundamentally different from the linear momentum, whose three components are simultaneously measurable.

**Can energy and angular momentum be measured precisely at the same time?**

6.3: The Three Components of Angular Momentum Cannot be Measured Simultaneously with Arbitrary Precision.

## Why is the commutator of angular momentum zero?

commutator of angular momentum operator to the position was zero (commut) if there wasn’t a component of the angular momentum that is equal to the position made by the commutation pair. While the results of the commutator angular momentum operator towards the free particle Hamiltonian indicated that angular momentum is the constant of motion. 1.

## Which is an example of commutation of Hamiltonian with momentum?

As shown by, e.g. Dirac in Lectures on Quantum Mechanics, any infinitesimal generator of a symmetry commutes with the Hamiltonian, which itself is the generator of time-translations, i.e. of the dynamics. Typical examples of an Hamiltonian that commutes with is the free particle, or more generally any admissible function of alone.

**How is angular momentum related to total energy?**

• Therefore angular momentum square operator commutes with the total energy Hamiltonian operator. With similar argument angular momentum commutes with Hamiltonian operator as well. • When a measurement is made on a particle (given its eigen function), now we can simultaneously measure the total energy and angular momentum values of that particle.

### How is the Hamiltonian operator represented in quantum mechanics?

The Hamiltonian operator for a quantum mechanical system is represented by the imaginary unit times the partial time derivative. The momentum is proportional to the gradient.