Spin-X Particles: What Does It Mean?

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Discussion Overview

The discussion revolves around the concept of spin in particles, specifically focusing on what it means when a particle or a composite system, such as a deuteron, is described as having a certain spin value (e.g., spin-1). Participants explore the implications of this designation in terms of total spin angular momentum, total angular momentum, and the nuances involved in composite systems.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the spin-X designation refers to total spin angular momentum, total angular momentum, or another concept.
  • Another participant explains that a deuteron, composed of two spin-1/2 particles, can have a total spin of 0 or 1, with the spin-1 state being a superposition of three states.
  • A different participant notes that for composite systems, spin can also refer to total angular momentum, which includes both orbital and spin contributions, and clarifies that the deuteron has both spin S and total angular momentum J equal to 1.
  • One participant simplifies the concept by stating that the "spin" of a particle represents the total angular momentum in its rest frame, while acknowledging that the calculation can be complex.

Areas of Agreement / Disagreement

Participants express varying interpretations of what spin-X means, with some agreeing on the definitions of spin and total angular momentum while others highlight the complexities and nuances involved. No consensus is reached regarding the precise implications of spin in this context.

Contextual Notes

Participants mention the need for a deeper understanding of quantum mechanics and the addition of spins, indicating that the discussion may depend on specific definitions and interpretations of angular momentum and spin in composite systems.

MixiesPLZ
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Sorry for this being a really general question but I am a bit confused what it means when it is stated that a particle or a bound state of several particles has a spin-X. For instance a deuteron is said to have spin-1.

Does this number refer to the total spin angular momentum, the total angular momentum, or something else that I am missing?
 
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Spin is a little bit tricky, and a course in QM usually involves a lecture or two about the addition of spin. A deuteron is made up of two spin-1/2 particles, so it can have a spin of 0 or 1, where a spin-0 state is when the spin number and the magnetic number are both 0 for both particles. The spin-1 state is actually a superposition of three states. In all three, both particles have s=1/2, and then the total m is given by summing the two different m's together. Remember that for s=1/2, m=-1/2 or 1/2, so if we take all the combinations of those three, we get all of the spin-1 states. Note that we can get M=0 either by adding 1/2 and -1/2, or by adding -1/2 and 1/2 (i.e. these are not distinguishable particles), so this state is also a superposition.

Check out http://itl.chem.ufl.edu/4412_u97/angular_mom/node10.html if you want some more details.
 
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when one talks of spin for a composite system, one can also mean the total angular momentum: sum of orbital and spin angular momentum.

But the deuteron has S = 1, and it has also J = 1 (J=S+L). So both spin S and 'nuclear spin" J is 1.

So it can have L = 0 or/and 2 (not L = 1 since then you would not have an antisymmetric wave-function)

http://en.wikipedia.org/wiki/Deuterium
 
In simple terms, the "spin" of particle is the total angular momentum it has in its rest system. Details of how it is calculated get more complicated.
 

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