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.

Prediction of Unified New Physics beyond Quantum Mechanics from the Feynman Path Integral: Elementary Cycles String Theory

We prove that the Feynman Path Integral is equivalent to a novel stringy description of elementary particles characterized by a single compact (cyclic) world-line parameter playing the role of the particle internal clock. This clearly reveals an exact unified formulation of quantum and relativistic physics, potentially deterministic, fully falsifiable having no fine-tunable parameters, also proven in previous pap,rs to be completely consistent with all known physics, from theoretical physics to condensed matter. New physics will be discovered by observing quantum phenomena with experimental time accuracy of the order of 10-2 sec.

The Schrödinger Equation, Path Integration and Applications

The Schrödinger equation is fundamental in quantum mechanics as it makes it possible to determine the wave function from energies and to use this function in the mean calculation of variables, for example, as the most likely position of a group of one or more massive particles. In this paper, we present a survey on some theories involving the Schrödinger equation and the Feynman path integral. We also consider a Feynman–Kac-type formula, as introduced by Patrick Muldowney, with the Henstock integral in the description of the expectation of random walks of a particle. It is well known that the non-absolute integral defined by R. Henstock “fixes” the defects of the Feynman integral. Possible applications where the potential in the Schrödinger equation can be highly oscillating, discontinuous or delayed are mentioned in the end of the paper.

Quantum mechanics and entropic gravity via the principle of stationary von Neumann entropy and quantropy

This paper utilizes the principle of stationary entropy to derive Feynman path integral formalism of quantum mechanics and entropic gravity formalism that recovers the Einstein field equations in the classical limit. For dynamics, the relevant concept of entropy is quantropy, proposed by John Baez et al. For statics, the relevant concept of entropy is von Neumann entropy.