Adjective
(set theory, order theory, of a binary relation R on a set S) Having the property that, for any two distinct elements of S, at least one is not related to the other via R; equivalently, having the property that, for any x, y ∈ S, if both xRy and yRx then x=y.
(of a tensor) That changes sign when any two indices are interchanged (e.g., Tijk = -Tjik);
(of a bilinear form) For which B(w,v) = -B(v,w).
(linear algebra, of certain mathematical objects) Whose sign changes on the application of a matrix transpose or some generalisation thereof:
(of a matrix) Whose transpose equals its negative (i.e., M = −M);
All 3 components of the dipole operator are antisymmetric under inversion with respect to the nucleus, : where is the dipole operator and is the inversion operator. Source: Internet
As a result, it can be regarded as an observable of the system, which means that, in principle, a measurement can be performed to find out if a state is symmetric or antisymmetric. Source: Internet
A more rigorous statement is that the total wave function for two identical fermions is antisymmetric with respect to exchange of the particles. Source: Internet
Approximated wavefunction of the deuteron The deuteron wavefunction must be antisymmetric if the isospin representation is used (since a proton and a neutron are not identical particles, the wavefunction need not be antisymmetric in general). Source: Internet
Conversely, if the diagonal quantities A(x,x) are zero in every basis, then the wavefunction component : is necessarily antisymmetric. Source: Internet
Equality is also the only relation on a set that is reflexive, symmetric and antisymmetric. Source: Internet