How composite particles have definite spin?

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Discussion Overview

The discussion revolves around the nature of spin in composite particles, particularly how their spin can be defined despite the spins of their constituent particles being in superpositions. Participants explore theoretical implications, examples, and the relationship between spin and energy states.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that a composite particle's spin is influenced by the spins of its constituent particles, which may not have definite spins due to superposition.
  • Another participant states that if the total spin commutes with the Hamiltonian, a particle in an eigenstate of energy will also be in an eigenstate of spin.
  • A question is raised regarding the nature of the particle's spin, specifically whether there is only one spin eigenstate or if it relates to the state with the least energy.
  • A participant expresses confusion about the previous explanations, indicating a lack of understanding.
  • References to external resources are provided to illustrate examples of spin states, particularly in hydrogen atoms.
  • One participant argues that hydrogen should be considered to have both spins 0 and 1, as it has multiple spin states.
  • Another participant clarifies that the spin of a composite particle is determined by both the spins and the orbital angular momentum of its constituents.
  • A question is posed about how the spin of the alpha particle is defined as 0, despite the possibility of superpositions.
  • It is mentioned that there are no excited states of the helium nucleus with higher spin, suggesting a limitation in the spin states available.
  • A participant asserts that the spin of the alpha particle is not merely considered to be 0, but is measured to be 0, linking it to the particle's binding energy and total Hamiltonian.

Areas of Agreement / Disagreement

Participants express differing views on how spin is defined for composite particles, particularly regarding the implications of superposition and the measurement of spin states. There is no consensus on the interpretation of spin in composite particles, and multiple competing views remain.

Contextual Notes

Some discussions hinge on the definitions of spin and the conditions under which certain states are considered. The relationship between spin and energy states is also a point of contention, with unresolved mathematical implications regarding superpositions.

ShayanJ
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Consider a composite particle. Its spin is determined by the spins of its constituent particles. But the constituent particles are in a superposition of different spin states and so don't have a definite spin. So it seems it shouldn't be possible to ascribe a definite spin to the composite particle. I know, one particular state may be the stable state but that only means this state is the most probable one and the composite particle is only mostly in that state, not always!
 
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A composite particle may or may not be in an eigenstate of spin. If the total spin commutes with the Hamiltonian, a particle in an eigenstate of energy will also be in an eigenstate of spin.
 
But what is that which is considered to be the partcile's spin?
I mean...there is only one spin eigenstate?
Or you're talking about the state with the least energy?
 
I don't understand anything you wrote.
 
Ok, Thanks to atyy, I can ask my question more clearly. In the first of atyy's files, the spin states of the hydrogen atom are mentioned. There are three states of spin 1 and one state of spin 0. So Hydrogen should have spins 0 and 1. You can't say its spin is 1 or 0. Its spin is both.
 
Shyan said:
Consider a composite particle. Its spin is determined by the spins of its constituent particles.
That's not true. The spin is the angular momentum in the rest frame of the center of mass (or energy in relativistic mechanics) of the particle. Therefore, also the orbital angular momentum of the particles contributes to it's spin. In contrast to an elementary particle, a compound particle may have several spin eigenvalues or be in a superposition of them. E.g. for an hydrogen atom (neglecting nuclear spin), the total spin J is the sum of the orbital momentum L and the spin of the electron S.
 
a compound particle may have several spin eigenvalues or be in a superposition of them.
That's exactly my point. My quesion is, while that is known, how is that e.g. spin of the [itex]\alpha[/itex] particle is considered to be 0? Why people ascribe a definite spin to it?
 
I suppose there are no, even metastable, excited states of the He nucleus with higher spin.
 
  • #10
It's not "considered to be 0". It's measured to be 0.

In any event, an alpha particle is a state of definite binding energy, and since total spin commutes with the total Hamiltonian, it's also in a state of definite total spin.
 

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