Feynman kernel analytical solutions for the deformed hyperbolic barrier potential with application to some diatomic molecules

In this paper, we derive the `-states energy spectrum of the q-deformed hyperbolic Barrier Potential. Within the Feynman path integral formalism, we propose an appropriate approximation of the centrifugal term. Then, using Euler angles and the isomorphism between S3and SU(1, 1), we convert the radial path integral into a maniable one. The obtained eigenvalues are in very good agreement with the numerical results. In addition, we applied our results to some diatomic molecules and obtained accurate results compared to the experimental (RKR) values.

The Vacuum-Phonon (Sonon) Reinterpretation of QED

This paper provides a reference copy of one particular and highly informal comment in a multiweek Academia.edu discussion of the paper Randomness in Relational Quantum Mechanics by Gary Gordon. The other main participants in this particular thread of the discussion were Doug Marman, Conrad Dale Johnson, Ruth Kastner, and the author. In this comment, the author argues that the only self-consistent approach to reconciling Feynman path integrals with Maxwell’s experimentally well-proven theory of electromagnetic wave pressure is introducing a new spin-0 particle, the vacuum or space phonon (sonon), that conveys linear momentum. The path histories of QED become the always-expanding structure of the sonon field, which, like a bubble, becomes increasingly unstable as it expands. The collection of all sonon fields around well-defined bundles of conserved quantum properties creates xyz space by defining the complete set of relational information for those entities. Spacetime in the sonon model is granular, multi-scale, and entirely mass-energy dependent. Implications of the sonon model are discussed, including the need for a drastic update to general relativity to take the multi-scale granularity of spacetime directly into account, rather than explaining it obliquely via models such as dark matter, dark energy, or MOND.

The Generalized Hamilton Principle and Non-Hermitian Quantum Theory

The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian quantum theory, i.e., the standard Schrodinger equation. In this paper, we have generalized the Hamilton principle to the generalized Hamilton principle, which can describe the open system (mass or energy exchange systems) and nonconservative force systems or dissipative systems, and given the generalized Lagrange function, it has to do with the kinetic energy, potential energy and the work of nonconservative forces to do. With the Feynman path integration, we have given the non-Hermitian quantum theory of the nonconservative force systems. Otherwise, with the generalized Hamilton principle, we have given the generalized Hamiltonian for the particle exchanging heat with the outside world, which is the sum of kinetic energy, potential energy and thermal energy, and further given the equation of quantum thermodynamics. PACS: 03.65.-w, 05.70.Ce, 05.30.Rt