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solas99
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why is only one component of angular momentum is quantised, and what determines which component is quantised?
Do you mean can not be simultaneously diagonalized? All three are quantized simultaneously.karlzr said:Different components of angular momentum do not commute, so they cannot be quantized at the same time. Of all the components, z component is the easiest to deal with.
An operator is a mathematical object that acts on a physical system to produce a result. In physics, operators are used to represent physical quantities such as position, momentum, and energy. They are an essential tool in studying the behavior of quantum systems.
The commutation of operators refers to the order in which operators act on a system. In quantum mechanics, the order of operations can affect the outcome of a measurement. This is known as the commutation relation, which describes how two operators behave when applied in different orders.
In general, operators do not commute under multiplication. This means that the order in which they are multiplied matters and can affect the final result. The commutation relation described earlier determines the behavior of operators under multiplication in quantum mechanics.
The commutation of operators is crucial in understanding the behavior of quantum systems. It allows us to predict the outcomes of measurements and determine the uncertainty in certain physical quantities. It also plays a role in the formulation of the Heisenberg uncertainty principle, which states that certain pairs of physical quantities cannot be simultaneously measured with arbitrary precision.
Yes, operators can be represented by matrices in many cases. In quantum mechanics, operators are typically represented by Hermitian matrices. The commutation relation between two operators can be expressed as a commutator, which is also a mathematical object that can be represented by a matrix.