0
$\begingroup$

I know that identical fermions have to have antisymmetric wave function. If I trap two electrons, one in a harmonic trap and other in a quartic trap. I can distinguish the electrons by which trap they belong to. Will the wave function of the two particles still be antisymmetric? Adding on to this, if I have two electrons of different mass (take it to be their effective mass) and put them in two different SHO with different angular frequency, ω so that the wave function turns out to be the same (the wave function for SHO only depends on the product of m and ω, so we can tune them). Now since the wave function of both the electrons will be the same (take it to be the ground state), can we call them identical particles OR will the wave function be antisymmetric?

$\endgroup$

1 Answer 1

1
$\begingroup$

The antisymmetric wave function for fermions is a consequence of particle indistinguishability. Therefore:

  • the two electrons in the two traps are still indistinguishable - there is no way to know which is which, only that one is in the harmonic and another is in the quartic traps.
  • the two electrons with different masses are not really identical particles - calling them both with the same word does not change this. Thus, they are distinguishable - e.g., by their mass.
$\endgroup$
3
  • $\begingroup$ In the second scenario, they have identical wavefunctions (even though the masses are different). Thinking in terms of that particles are completely described by their wavefunction, I feel that they are identical. $\endgroup$
    – Aman Anand
    Commented Jan 12, 2022 at 13:07
  • $\begingroup$ Can you link some references for me to read up on these and be more clear? $\endgroup$
    – Aman Anand
    Commented Jan 12, 2022 at 13:08
  • 1
    $\begingroup$ Any quantum mechanics textbook discusses this: I suggest looking in ther chapters dealing with the Pauli exclusion principle, and Quantum statistics. The one in Landau&Livshits could be perhaps more revealing. Related discussions can be also found in statistical physics texts. Identical means identical in everything, including their masses. Whether we can have two particles with completely identical properties but different masses is probably answered by more advanced quantum theory. $\endgroup$
    – Roger V.
    Commented Jan 12, 2022 at 13:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.