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lion8172
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When we set the raising and lowering operators for spin to be [tex]S_{\pm} = S_x \pm i S_y[/tex], what convention are we following (i.e. why is the first term taken to be S_x and the second taken to be S_y)?
lion8172 said:When we set the raising and lowering operators for spin to be [tex]S_{\pm} = S_x \pm i S_y[/tex], what convention are we following (i.e. why is the first term taken to be S_x and the second taken to be S_y)?
Raising and lowering operators for spin are mathematical operators used in quantum mechanics to describe the angular momentum of a particle. They are denoted as S+ and S- and are used to raise or lower the spin state of a particle.
Raising and lowering operators for spin work by acting on a spin state to change its value. The S+ operator increases the spin by one unit, while the S- operator decreases the spin by one unit.
The commutation relationship between the raising and lowering operators for spin is given by [S+, S-] = Sz, where Sz is the z-component of the spin angular momentum operator. This relationship is a fundamental property of spin operators in quantum mechanics.
Raising and lowering operators for spin are significant in quantum mechanics because they allow us to describe and manipulate the spin state of a particle. They also play a crucial role in the understanding of quantum systems, such as atoms and nuclei, which have intrinsic spin.
In experiments, raising and lowering operators for spin are used to measure the spin of a particle and to manipulate its state. They are also used to study the behavior of quantum systems and to develop new technologies, such as quantum computing.