The Wavefunction Of Many-Particle Systems Viewed Through Systemic Functional Linguistics

Penrose (2004: 580):

How, then, are we to treat many-particle systems according to the standard non-relativistic Schrödinger picture? As described [previously], we shall have a single Hamiltonian, in which all momentum variables must appear for all the particles in the system. Each of these momenta gets replaced, in the quantisation prescription of the position-space (Schrödinger) representation, by a partial differentiation operator with respect to the relevant position coordinate of that particular particle. All these operators have to act on something and, for consistency of their interpretation, they must all act on the same thing. This is the wavefunction. As stated above, we must indeed have one wavefunction Ψ for the entire system, and this wavefunction must indeed be a function of the different position coordinates of all the separate particles.

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From the perspective of Systemic Functional Linguistic Theory, the wavefunction identifies the potential of a quantum system: all the probable locations of all the particles that are instances of that systemic potential.