On the Quantum Potential

M. R. Brown

This paper investigates the composition of the quantum potential and explores its role in the breakdown of symplectic symmetry in quantum mechanics. General expressions are derived for the quantum potential in both configuration space and momentum space representations. By comparing the configuration space and momentum space representations of the causal interpretation of quantum mechanics, the quantum potential is shown to break the symplectic symmetry that exists between these two representations in classical mechanics. It is shown that the quantum potential in configuration space may be expressed as the sum of a momentum dispersion energy and a spatial localisation energy. The quantum potential is thus shown to represent the solely quantum aspects of quantum systems. The composition and role of the quantum potential is analysed for a particle in a linear potential and for two eigenstates of the quantum harmonic oscillator.

Robert Carroll

Eric Hand

M. R. Brown

The composition of the quantum potential and its role in the breakdown of classical symplectic symmetry in quantum mechanics is investigated. General expressions are derived for the quantum potential in both configuration space and momentum space representations. By comparing the configuration space and momentum space representations of the causal interpretation of quantum mechanics, the quantum potential is shown to break the symplectic symmetry that exists between these two representations in classical mechanics. In addition, it is shown that the quantum potential in configuration space may be expressed as the sum of a momentum dispersion energy and a spatial localisation energy; a complementary expression for the quantum potential being found in the momentum representation. The composition and role of the quantum potential in both representations is analysed for a particle in a linear potential and for two eigenstates of the quantum harmonic oscillator.

Jincheng Zhang

Quantum Potential Adaptive Computation explores the potential of leveraging quantum potential fields for enhanced computational capabilities. This research introduces a novel framework predicated on quantum potential self-similarity, aiming to automate complex quantum computations through dynamic parameter adjustment. The core mechanism centers around a self-consistent update of the quantum potential, iteratively refining the system's state to achieve desired results. This approach offers a pathway towards simplified and more efficient quantum algorithm design, particularly for problems exhibiting intricate quantum dynamics. We present a preliminary model demonstrating the potential of this framework, highlighting its advantages over traditional methods in certain scenarios. This work investigates the design of a quantum potential adaptive computation framework, outlining its theoretical foundation and preliminary experimental validation.