we assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the dirac matrices. then by making use of a suitable ansatz, the dirac equation has a very simple solution which is exact. we then have calculated the static properties of the nucleon in the ground...

In this study, we assume that the brain uses a general-purpose pattern generator to transform static commands into basic movement segments. We hypothesize that this pattern generator includes an oscillator whose complete cycle generates a single movement segment. In order to demonstrate this hypothesis, we construct an oscillator-based model of movement generation. The model includes an oscilla...

We prove approximate controllability of the bilinear Schrödinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant spectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the Galerkin approximations and...

Recently, an application of the numerical bootstrap method to quantum mechanics was proposed, and it successfully reproduces eigenstates various systems. However, is unclear why this works. In order understand question, we study in harmonic oscillators. We find that problem reduces Dirac's ladder operator exactly solvable analytically. Our result suggests may be regarded as a version approach e...

The relativistic harmonic oscillator represents a unique energy-conserving oscillatory system. detailed characteristics of the solution this are displayed in both weak- and extreme-relativistic limits using different expansion procedures, for each limit. In weak-relativistic limit, Normal Form is developed, which yields an approximation to that significantly better than traditional asymptotic p...