Closure property for many-particle wave functions

Walter Greiner, Ludwig Neise, Horst Stöcker B

Guangye Chen

Particle in one dimensional potential well demonstrates typical quantum mechanical behaviors determined by the related Schrodinger equation. The problem is solved here with a quasi-classical particle model that qualifies for quantum wave description. Our results cover majority of previous conclusions and reveal new mechanisms that, closure of the particle’s trajectory leads to quantization and lateral projections of particle’s three dimensional trajectories generate the Schrodinger wave functions for different energies. We explain that, Schrodinger wave functions represent different modes of particle’s motion and their amplitudes might measure the probability density that the particle is to be observed, but their interference invalids the probabilistic implication.

Lasse Kragh Sørensen

The minimum parameterization of the wave function is derived for the time-independent many-body problem. In this parameterization all electrons and electron pairs are indistinguishable which eliminates the exponential scaling with the number of particles plaguing all other correlation methods. An exponential scaling shown to stem from the expansion of the wave function in one-particle basis sets. It is demonstrated that using a geminal basis with a skew-symmetric orthogonal coefficient matrix, which fulfill a Lie algebra, the parameterization of the exact wave function becomes independent of the number of particles and only scale quadratic with the number of basis functions in the optimized basis and quartic in an arbitrary basis. The resulting antisymmetrized geminal power wave function is shown to fulfill the necessary and sufficient conditions for the exact wave function, treat all electrons and electron pairs as indistinguishable and be the most compact representation of the exact wave function possible. The number of parameters in the antisymmetrized geminal power wave function is exactly the same number of parameters as in the two-particle reduced density matrix thereby showing that these representations are equivalent just like the representations for a one-particle Hamiltonian. A detailed discussion of how the most compact wave function can be derived in general is also presented along with different geminal ansatze and sufficient closure relations. Due to the breaking of the scaling wall for the exact wave function it is expected that, if a general set of constraints can be found, even systems of biological relevance can be treated exactly in the future.

Mattia Walschaers

Andrii Myshko

We develop a structural reinterpretation of the foundational ontological problems of quantum mechanics within the program of Metamonism [1] and its physical extension Basic Ontodynamics [2]. Three ontological placeholders that have resisted satisfactory interpretation for a century — wave function collapse, wave-particle duality, and virtual particles — are identified as symptoms of a foundational gap: the absence of a structural account of what quantum objects are. The present framework proposes that quantum objects are activation regimes of the F-hierarchy at different degrees of F7 closure. The photon is F56 without F7 — an unclosed coherence regime. The electron is F56 with residual St closure. Wave-particle duality dissolves: there is one object at different closure states, not two natures. Collapse dissolves: measurement is a continuous F7 closure process driven by structural resonance, not a discontinuous transition. Virtual particles dissolve as ontological entities: interactions are direct F56 coherence redistributions through the shared background F123, with virtual particles as mathematical parametrizations of transient incomplete F7 closures. The uncertainty principle receives a structural reading: ∆x · ∆p and ∆E · ∆t are two aspects of the single constraint that F7 closure and F56 phase sharpness cannot be simultaneously maximal. Renormalization is identified as a symptom of ontological incompleteness: it compensates for the point particle idealization, the free propagator treatment of virtual particles, and the empty vacuum assumption— all of which the F-hierarchy framework replaces structurally. Five falsifiable predictions are stated: finite duration of atomic transitions, natural ultraviolet cutoff in vacuum fluctuations, vacuum birefringence at high laser intensity, confinement scale from F7 closure geometry, and renormalization group fixed points as F7 closure transitions. The paper is a programmatic contribution within Metamonism: it proposes a structurally unified ontological reading of quantum phenomena and establishes a research program in which the formal derivation of quantum mechanics from F-hierarchy dynamics becomes a well-posed task.