Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.

Nonlinear Modes of a Macroscopic Quantum Oscillator

Abstract: We consider the Bose-Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe, analytically and numerically, its collective modes - a nonlinear generalisation of the (symmetric and antisymmetric) Hermite-Gauss eigenmodes of a harmonic quantum oscillator.

Clarification of the electronic asymmetry in Π‐state Λ doublets with some implications for molecular collisions

Abstract: The asymmetry of the orbital part of the electronic wave functions and electronic charge distributions in 1Π, 2Π, and 3Π Λ doublets is carefully examined, to clear up considerable past confusion on this subject. The results are: (1) For 1Π and 3ΠΩ=1 states the electronic wave function in the e Λ‐doublet levels is symmetric with respect to reflection in the plane of rotation of the molecule and, in the f levels, antisymmetric. (2) For 2Π and 3Π0,2 states, in the Hund’s case (a) limit the electronic distributions in both Λ‐doublet levels are cylindrically symmetric. (3) As the case (b) limit is approached, the F1 e and F2 f wave functions of a 2Π state acquire an increasing degree of symmetric character with respect to reflection in the plane of rotation, while the F1 f and F2 e levels acquire antisymmetric character. In a 2Σ+–2Π radiative transition, the main branch P and R lines probe 2Π levels which are symmetric with respect to reflection in the plane of rotation while the main branch Q lines probe leve...

Permutation Symmetry of Many-Particle Wave Functions

Abstract: The symmetrization postulate (SP) states that wave functions are either completely symmetric or completely antisymmetric under permutations of identical particles. It is shown by one-dimensional counter-examples that SP is not demanded by the usual physical interpretation of the mathematical formalism of wave mechanics unless one makes use of further physical properties of real systems; the error in a standard proof of SP which ignores these properties is pointed out. It is then proved that SP is true for those systems of spinless particles which have the following properties: (a) probability densities are permutation-invariant, (b) allowable wave functions are continuous with continuous gradient, (c) the $3n$-dimensional configuration space is connected, (d) the Hamiltonian is symmetric, and (e) the nodes of allowed wave functions have certain properties. The counterexamples show that SP is not a necessary property of those systems which do not have property (c). The proof is extended to particles with internal degrees of freedom (including spin) by noting that any observable commutes with every permutation and making use of a particular observable acting only on internal variables. Extraneous mathematical assumptions, such as that of the existence of a "complete" set of commuting observables, criticized by Messiah and Greenberg, are not employed. Some comments are made on the conventional nature of the concept of identity for similar particles; the equivalence between the usual formulation in which different species of similar particles are treated as distinct, and that in which they are regarded as identical particles in different internal states, is emphasized.