aaaa202 said:Spin or angular momentum in my book is formulated in the basis of eigenstates of the operator that measures the angular momentum along the z-axis. But in principle I guess this could just as well have been done in the basis of eigenstates of Ly or Lx. Will that change anything in the equations? For example for spin where all vectors and matrices are written in basis of the eigenstates of Sz.
Relabeling spin or angular momentum operators is a process in quantum mechanics where the basis states of a system are changed by relabeling them with different quantum numbers. This is done to simplify calculations and better describe the system.
Relabeling spin or angular momentum operators is important because it allows for a more convenient and concise description of the quantum system. It also helps to better understand the properties and behavior of the system.
Relabeling spin or angular momentum operators is done by applying mathematical transformations to the original basis states of the system. These transformations can involve changing the labels of the basis states, reordering them, or combining them in different ways.
One example of relabeling spin or angular momentum operators is the transformation from Cartesian coordinates to spherical coordinates. This involves relabeling the basis states of a system from (x, y, z) to (r, θ, φ). Another example is the transformation from the spin-up and spin-down basis states to the +z and -z basis states.
Relabeling spin or angular momentum operators can lead to a simpler and more intuitive description of the quantum system. It can also make calculations and predictions easier and more accurate. Additionally, relabeling can reveal new symmetries and relationships within the system.