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hokhani
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- TL;DR Summary
- The project of spin on real space
If the spin space is independent of the real space, what is the meaning of, for example, the z-component of the spin?
The z-component of spin is a measurable quantity. The abstract spin vectors describe the spin state, but the spin operators represent real observables.hokhani said:Summary:: The project of spin on real space
If the spin space is independent of the real space, what is the meaning of, for example, the z-component of the spin?
hokhani said:the spin space is independent of the real space
Do you mean that there is something of real-rotation entity in spins?PeterDonis said:It isn't. The spin degrees of freedom are independent of the configuration space (position and momentum) degrees of freedom. But the spin operators are still connected to directions in real space.
hokhani said:Do you mean that there is something of real-rotation entity in spins?
Spin in real space refers to the intrinsic angular momentum of a particle, which is a fundamental property of all elementary particles. It is a quantum mechanical property that cannot be directly observed, but its effects can be measured.
The Z-component of spin represents the projection of the spin angular momentum onto the Z-axis in real space. It is one of the three components of spin, along with the X and Y components, and it determines the orientation of the spin axis in relation to the Z-axis.
Spin in real space refers to the physical orientation of the spin axis, while spin in spin space refers to the mathematical representation of the spin state. In other words, spin in real space is the actual direction of the spin, while spin in spin space is the abstract concept used to describe it.
The Z-component of spin is significant because it is one of the quantum numbers that can be used to describe a particle's state. It is also important in determining the behavior of particles in magnetic fields, as the Z-component of spin can interact with the magnetic field to produce a magnetic moment.
Yes, the Z-component of spin can change in certain situations, such as when a particle interacts with a magnetic field or when it undergoes a quantum measurement. However, the total spin of a particle, which is the combination of all three components, remains constant.