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General Forms of Wave Functions for Dipositronium, Ps2

David M. Schrader

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The consequences of particle interchange symmetry for the structure of wave functions of the states of dipositronium was recently discussed by the author [I]. In the present work, the methodology is simply explained, and the wave functions are explicitly given.

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It is demonstrated that in a system of NNN similar particles, the permissible wave functions are either symmetrical or antisymmetrical with respect to interchanges of the particles, if the following principles are assumed to be valid: (1) The interchange of two like particles produces no change in any measurable property of the system. In particular, if $\ensuremath{\psi}$ is to be a permissible wave function, $\ensuremath{\psi}\overline{\ensuremath{\psi}}$ must be unaltered by such an interchange. (2) All the wave functions obtained from a given permissible wave function by permuting the similar particles are also permissible wave functions for the same eigenvalue.
Symmetry has imposed very strong constraints on the internal structure of quantum mechanical system. In particular, whether a state can access a given outgoing channel is constrained by symmetry. For the dipositroniums, the most important channel is the Ps-Ps channel. However, based on symmetry consideration it was found that only a few excited states are allowed to access the Ps-Ps channel, thereby at least the existence of two higher L = 0 bound states (higher than the Ps-Ps threshold) has been affirmed.
The linear Zeeman effect in the molecular positronium Ps2 (dipositronium) is predicted for some of S=1S=1S=1, M=±1M=\pm1M=±1 states. This result is opposite to the case of the positronium atom; the latter has only quadratic Zeeman effect.