What hamiltonian ? The hamiltonian of the free particle ? Of the harmonic oscillator ? Of the hydrogen atom ?Feynmanfan said:How can I prove that the Hamiltonian commutes with the angular momentum operator?
In spherical coordinates it is straightforward but I'd like to understand the physical meaning of it.
Thanks.
Angular momentum is a physical quantity that represents the rotational motion of a system. It is defined as the product of the moment of inertia and the angular velocity of the system.
When two quantities commute, it means that they can be measured simultaneously without affecting each other. In the context of physics, this means that the values of these two quantities can be known with certainty at the same time.
The fact that angular momentum commutes with Hamiltonian is a fundamental property of quantum mechanics. It allows for the conservation of angular momentum, which is crucial in understanding the behavior of particles and systems at the atomic and subatomic level.
The commutation of angular momentum and Hamiltonian is related to Heisenberg's uncertainty principle through the mathematical relationship between the two. The uncertainty principle states that the more precisely the angular momentum of a particle is known, the less precisely its Hamiltonian (energy) can be known, and vice versa.
Yes, the commutation of angular momentum and Hamiltonian has been observed in various physical systems, such as atoms, molecules, and subatomic particles. This property has been confirmed through experiments and is essential in understanding the behavior of these systems.