spookyfish said:ok, but for a given m - some of them might not be possible
Angular momentum is a fundamental physical property that describes the rotational motion of an object around an axis. It is important in physics because it helps us understand the behavior of objects in motion, such as planets orbiting around a star or electrons spinning around an atom.
Angular momentum states refer to the different possible states that an object can have based on its angular momentum. Clebsh-Gordan coefficients are mathematical values that describe the probability of an object transitioning from one angular momentum state to another. They are related because the values of the coefficients depend on the specific angular momentum states involved.
Clebsh-Gordan coefficients are used in quantum mechanics to describe the behavior of subatomic particles, such as electrons. They help us understand how these particles transition between different angular momentum states, which is crucial in understanding their behavior and interactions with other particles.
The selection rule is a principle in quantum mechanics that states that certain transitions between angular momentum states are allowed while others are forbidden. This rule helps us determine which Clebsh-Gordan coefficients are non-zero and therefore contribute to the overall probability of a transition occurring.
Clebsh-Gordan coefficients are calculated using mathematical formulas that take into account the angular momentum values of the initial and final states. These coefficients can be affected by factors such as the spin of the particles involved, the strength of their interactions, and the presence of external fields.