Slater Determinant & Permanent

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SUMMARY

The discussion clarifies the use of Slater determinants and permanents in quantum mechanics to identify symmetrical and anti-symmetrical states. A Slater determinant is employed for fermionic systems, ensuring the wave function is totally antisymmetric, while a permanent is used for bosonic systems, resulting in a totally symmetric wave function. The presence of minus signs indicates a determinant, whereas the absence signifies a permanent. This distinction is crucial for constructing appropriate wave functions in quantum systems.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with fermionic and bosonic systems
  • Knowledge of wave function properties
  • Basic grasp of linear algebra concepts, particularly determinants and permanents
NEXT STEPS
  • Study the mathematical properties of Slater determinants in quantum mechanics
  • Explore the role of permanents in bosonic systems
  • Learn about antisymmetry and symmetry in wave functions
  • Investigate applications of determinants and permanents in quantum chemistry
USEFUL FOR

Students and professionals in quantum mechanics, physicists working with particle systems, and researchers focusing on wave function analysis will benefit from this discussion.

M. next
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How to use Slater determinant and permanent to find out whether the state is symmetrical or anti-symmetrical?
How to use them? I got the concept but I didn't get for example when to know if there was a plus or a minus and thus whether what we're talking about is a permanent or determinant (respectively).
 
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If you have minus signs, its a determinant and totally antisymmetric, if you don't, it's a permanent and totally symmetric.

It's not something you determine. It is something you put into your ansatz: You choose determinants as a basis set for fermionic systems precisely because you know that you need an antisymmetric wave function, and determinants are the simplest kinds of wave functions which are totally antisymmetric. And for the same reason you choose permanents as basis for bosonic systems because they are the simplest wave functions which are totally symmetric.
 
Thank you a lot for clearing things up. I thought it is something to be determined.
 

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