Fermions in bound states and their wavefunctions

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Discussion Overview

The discussion revolves around the properties of wavefunctions for two spin-half fermions in a bound state, focusing on the implications of their total spin and the symmetry of their overall wavefunction. Participants explore concepts related to fermionic behavior, symmetry, and the nature of bound states in quantum mechanics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether the total wavefunction must be antisymmetric due to the fermionic nature of the particles, or if it could be symmetric because the total spin corresponds to a bosonic state.
  • Another participant asserts that a bound state of an even number of fermions is a boson, suggesting that the overall wavefunction is symmetric.
  • A different participant corrects an earlier claim, stating that the spin-0 state is antisymmetric while the spin-1 state is symmetric.
  • There is confusion expressed regarding the relationship between symmetry, parity, and the specific states of the particles, with a participant questioning the application of parity in this context.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the symmetry properties of the wavefunctions associated with the spin states of the fermions. There is no consensus on whether the total wavefunction should be considered symmetric or antisymmetric.

Contextual Notes

Participants reference concepts such as parity and the nature of bound states, indicating potential limitations in their understanding of how these concepts apply to the symmetry of wavefunctions for fermions.

ZombieCat
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Hello all,

This may be my very first post on Physics Forums. I am a 1st year physics grad student and need some help on something that's been bugging me. Suppose we have two spin half particles in a bound state. The total spin will either be 0 or 1. The spin 0 state, for example, would be symmetric (even parity right?) so it would need an antisymmetric spatial wavefunction to make the overall wavefunction antisymmetric since we have fermions? But then I thought the overall wavefunction may be symmetric because the total spin is that of a boson?

Rephrased, my question is this: would the total wavefunction have to be antisymmetric since we are dealing with fermions, or would it be symmetric since the total spin is that of a boson?
Which is it and why?

If we came along and didn't know that there were two fermions in there would we think it was a boson?

Does the fermions being in a bound state matter? What about the shape of the potential?
 
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Welcome to PF!

Hello ZombieCat! Welcome to PF! :smile:
ZombieCat said:
Hello all,

This may be my very first post on Physics Forums.

uhhh? :confused: did you use to be Schrödinger's cat? :biggrin:
… Rephrased, my question is this: would the total wavefunction have to be antisymmetric since we are dealing with fermions, or would it be symmetric since the total spin is that of a boson?
Which is it and why?

If we came along and didn't know that there were two fermions in there would we think it was a boson?

It's symmetric because it is a boson …

a bound state of an even number of fermions is a boson.

That's why mesons are bosons, but protons and neutrons are fermions … they're two quarks and three quarks respectively! :wink:
 
ZombieCat said:
Suppose we have two spin half particles in a bound state. The total spin will either be 0 or 1. The spin 0 state, for example, would be symmetric (even parity right?)
Sorry, wrong. The spin-0 state is antisymmetric, and the spin-1 state is symmetric.
 


Haha! I guess this zombie cat USED to be Schrödinger's cat, but is now the quantum mechanically undead. Thanks Tiny Tim!

As for the symmetry of the spin-0 state, (ud-du)/sqrt(2), I understand that the spins are opposed to make this happen and this state should be antisymmetric... I guess I'm getting confused about the difference between symmetry and parity, (-1)^L. Does this not apply here? Why not?
 

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