I know what are Hermitian operators and anti-hermitian operators.but as i have studied quantum mechanics most of the operators we had dealt with them are hermitian and this question popped up in my mind that does any anti-hermitian operator exists in quantum mechanics?

  • 1
    $\begingroup$ Sure, all exponents in unitary operators are firmly antihermitean. $\endgroup$ Oct 2, 2020 at 14:53
  • 5
    $\begingroup$ If $A$ is anti-hermitian then $H = i A$ will be hermitian, so when anti-hermitian operators do arise we will often choose to consider equivalent hermitian ones instead $\endgroup$ Oct 2, 2020 at 14:57
  • $\begingroup$ Exactly, in standard QM you put an extra "i" in front of an Hermitean operator to have the exponent of the unitary one. Operator are regarded as "observables", so you want real spectra (hence Hermitean stuff). $\endgroup$
    – Quillo
    Oct 2, 2020 at 15:01
  • $\begingroup$ Possible duplicate: physics.stackexchange.com/q/82613/2451 $\endgroup$
    – Qmechanic
    Oct 2, 2020 at 16:28


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