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annaphys
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In quantum mechanics one sees what J^2 can offer but why do we even consider looking at the eigenstates and eigenvalues of J^2 and a component of J, say J_z? Why don't we just use J?
annaphys said:why do we even consider looking at the eigenstates and eigenvalues of J^2 and a component of J, say J_z? Why don't we just use J?
##J^2## is easier to work with because it's defined as ##J^2 = J_x^2 + J_y^2 + J_z^2##. You could try to work with ##J = \sqrt{J^2}## as the magnitude of total AM, but I suspect it would be more awkward to work with.annaphys said:So the only reason we use J^2 is because it's a scalar?
Angular momentum is a measure of an object's rotational motion. It is defined as the product of an object's moment of inertia and its angular velocity.
The squared of the angular momentum is important because it represents the magnitude of the angular momentum vector. This value is conserved in a closed system, meaning it remains constant even as the object's rotational speed and direction change.
Angular momentum is related to conservation of energy through the principle of conservation of angular momentum. This principle states that in a closed system, the total angular momentum remains constant, which also means that the total energy remains constant.
Angular momentum has many practical applications in fields such as physics, engineering, and astronomy. For example, it is used in the design of vehicles and machinery that involve rotational motion, and it is also important in understanding the motion of planets and other celestial bodies.
Angular momentum can be calculated using the formula L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity. It can also be measured using various instruments such as a gyroscope or a rotational motion sensor.