Spin angular momentum of a spin-1 particle

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Discussion Overview

The discussion revolves around the calculation of spin angular momentum for a spin-1 particle in quantum mechanics, specifically examining the formula used and its application to different spin values.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant presents the formula for spin angular momentum, S = √(s(s+1))ℏ, and applies it to a spin-1/2 particle, calculating S = ((√3)/2)ℏ.
  • The same participant questions whether the formula yields S = √2ℏ for a spin-1 particle.
  • Another participant asks if there is skepticism regarding the arithmetic involved in the calculations.
  • A different participant asserts that the formula is a general relationship applicable to all types of angular momentum in quantum mechanics, providing examples for spin, orbital, and total angular momentum.
  • One participant expresses gratitude for the clarification provided in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific value of spin angular momentum for a spin-1 particle, and there is no resolution regarding the arithmetic or the application of the formula.

Contextual Notes

Participants reference the general formula for angular momentum without resolving the implications of applying it to different spin values, and there may be assumptions about the validity of the arithmetic that are not explicitly stated.

liometopum
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The spin angular momentum of a spin 1/2 particle is given by S = √(s(s+1))ℏ. If s =1/2,
S= ((√3)/2)ℏ

So, if s=1 is S= √2ℏ ?
 
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Do you have some reason to be skeptical of the arithmetic?
 
Not at all. Every source I checked to confirm it only gave S for spin-1/2. Thanks!
 
It's a general relationship that applies to all kinds of angular momentum in QM.

Spin angular momentum: ##S = \sqrt{s(s+1)} \hbar##

Orbital angular momentum: ##L = \sqrt{l(l+1)} \hbar##

Total (spin + orbital) angular momentum: ##J = \sqrt{j(j+1)} \hbar##
 
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Thanks so much for helping clarify this!
 

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