A mathematical model for the slit-experiments in the heart of quantum mechanics is developed to gain insight in quantum theory.
The proposed system-theoretical approach of the mathematical model takes a different route compared to matrix mechanics in complex vector spaces: it is entirely based on commutative mathematics, eg. convolution, integral transformations and starts with spacetime functions with inherent energy based cause and effect relations of the statefunction Ѱ in the complex Hilbert space.
The benefits of his approach are
The model predicts the patterns in the experiments with mathematical functions of the energy distributions. The quantum mechanical description of physical reality of slit experiments thus may be considered complete in the sense and requires the thought experiment of reality still, which is not contradictory with the exact results.
At quantum slit-experiment energy level, the patterns found in double slit experiments actually are found to be an effect of energy (amplitude-) modulation. An equivalent double-slit pattern can be retrieved from an input modulated 1-slit experiment; two distributions in the (k-space) energy frequency domain appear mathematically as if produced by two slits, ánd the relation between k0 and the physical slits is unambiguous. Due to the absence of multiple slits this excludes interference interpretations (of particles, waves). In principle it may be possible to experimentally verify the effect with a modulated input function of a one-slit experiment.
The system-theoretical method uses well known generic properties of quanta and evolves into determinism in quantum mechanics slit experiments, without a direct observation/measurement or direct description with variables of the individual quanta at the heart of the state-function Ѱ.
The mathematics in the system theoretical approach handles beables by treatment of momentum p in system theoretical I/O relations of the transformed functions and allows the proposed description by the avoidance of a direct addressing of the individual quanta through variables. The followed method yields exact, non-probabilistic results.
