# Understanding Spin Basis & Representation in Modern Physics | Explained

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• yeezyseason3
In summary: The spin states are all orthogonal to each other, so they aren't the same state. In summary, spin can be represented in different coordinate systems using mathematical methods, similar to how a position can be described in different ways using different coordinate systems. The Pauli exclusion principle does not prevent the partial superposition of spin states, as they are orthogonal and not the same state.
yeezyseason3
So I am in an introductory modern physics class and we discussed how intrinsic spin can be a linear combination of the spin basis. I am a bit confused on the physical representation of this and whether or not there are different basis to represent spin. If it is possible, what would be the point of doing so and how would you do it? From what I am understanding, spin can be treated like a coordinate system and you can use basic mathematical methods to represent spin in another coordinate system. Another question comes with the partial superposed spin states of an eigenstate. Doesn't the Pauli exclusion principle prevent this from happening?

yeezyseason3 said:
I am a bit confused on the physical representation of this and whether or not there are different basis to represent spin. If it is possible, what would be the point of doing so and how would you do it?
It's analogous to the way that I can describe the position of something as "one kilometer to the north and one kilometer to the east" or as "1.414 kilometers northeast, zero kilometers northwest". The first description is more convenient if I'm looking at a map with north up and north/south and east/west gridlines on it; the second is more convenient if I'm in a city whose streets are laid out in a grid pattern with downtown/uptown avenes running from southwest to northeast and crosstown streets at right angles to the avenues. One way, my basis vectors are north/east, the other ways they're uptown/crosstown. But it's the same point with the same physical relationship to me either way.

The key here is that spin states are mathematically a kind of vector, and a vector can always be written as the sum of other vectors in many different ways - but it's still the same vector.

From what I am understanding, spin can be treated like a coordinate system and you can use basic mathematical methods to represent spin in another coordinate system. Another question comes with the partial superposed spin states of an eigenstate. Doesn't the Pauli exclusion principle prevent this from happening?
No. The Pauli exclusion principle says that no two particles can be in the exact same state, but here we have one particle with one state, and we're just playing with the mathematical fact that the state is a vector so can be written as the sum of other vectors.

Re your first question, spin states are essentially vectors, and any vector can be expressed in any basis. There's no more to it than that.

I don't understand why the Pauli exclusion principle would come into it.

## 1. What is spin in physics?

Spin is an intrinsic property of subatomic particles, such as electrons, protons, and neutrons. It is a form of angular momentum that does not arise from the particle's motion, but is instead an inherent property of the particle itself.

## 2. How is spin measured in physics?

In physics, spin is measured in units of angular momentum, usually expressed as multiples of Planck's constant. The spin of a particle can be determined through experiments, such as scattering experiments, which measure the angular momentum transfer between the particles involved.

## 3. What is the significance of spin in modern physics?

Spin plays a crucial role in our understanding of the fundamental laws of nature. It is a fundamental property of matter and is used to explain various phenomena, such as magnetism and the stability of atoms. It also has practical applications, such as in spintronics and quantum computing.

## 4. What is the spin-basis representation in modern physics?

The spin-basis representation is a mathematical framework used to describe the spin of particles. It uses a set of basis vectors to represent the possible orientations of a particle's spin, and these vectors can be combined to describe the overall spin state of a particle.

## 5. How does understanding spin representation help in modern physics research?

Understanding spin representation is essential in modern physics research as it allows scientists to describe and predict the behavior of particles with spin. It also helps in developing new theories and technologies, such as quantum computing, that rely on the manipulation of particle spin.

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