Disguised electromagnetic connections in classical electron theory

In the first quarter of the 20th century, physicists were not aware of the existence of classical electromagnetic zero-point radiation nor of the importance of special relativity. Inclusion of these aspects allows classical electron theory to be extended beyond its 19th century successes. Here we review spherical electromagnetic radiation modes in a conducting-walled spherical cavity and connect these modes to classical electromagnetic zero-point radiation and to electromagnetic scale invariance. Then we turn to the scattering of radiation in classical electron theory within a simple approximation. We emphasize that, in steady-state, the interaction between matter and radiation is disguised so that the mechanical motion appears to occur without the emission of radiation, even though the particle motion is actually driven by classical electromagnetic radiation. It is pointed out that, for nonrelativistic particles, only the harmonic oscillator potential taken in the low-velocity limit allows a consistent equilibrium with classical electromagnetic zero-point radiation. For relativistic particles, only the Coulomb potential is consistent with electrodynamics. The classical analysis places restrictions on the value of e^2/(hbar c).

Extended study on the application of the sextic potential in the frame of X(3)-Sextic

The main aim of the present paper is to study extensively the γ-rigid Bohr Hamiltonian with anharmonic sextic oscillator potential for the variable β and γ = 0. For the corresponding spectral problem, a finite number of eigenvalues are found explicitly, by algebraic means, so-called Quasi-Exact Solvability (QES). The evolution of the spectral and electromagnetic properties by considering higher exact solvability orders is investigated, especially the approximate degeneracy of the ground and first two β bands in the critical point of the shape phase transition from a harmonic to an anharmonic prolate β-soft, also the shape evolution within an isotopic chain. Numerical results are given for 39 nuclei, namely, 98-108Ru, 100-102Mo, 116-130Xe, 180-196Pt, 172Os, 146-150Nd, 132-134Ce, 152-154Gd, 154-156Dy, 150-152Sm, 190Hg and 222Ra. Across this study, it seems that the higher quasi-exact solvability order improves our results by decreasing the rms, mostly for deformed nuclei. The nuclei 100,104Ru, 118,120,126,128Xe, 148Nd and 172Os fall exactly in the critical point.

Fundamental energy scale of the thick brane in mimetic gravity

In this paper, thick branes generated by the mimetic scalar field with Lagrange multiplier formulation are investigated. We give three typical thick brane background solutions with different asymptotic behaviors and show that all the solutions are stable under tensor perturbations. The effective potentials of the tensor perturbations exhibit as volcano potential, Poöschl–Teller potential, and harmonic oscillator potential for the three background solutions, respectively. All the tensor zero modes (massless gravitons) of the three cases can be localized on the brane. We also calculate the corrections to the four-dimensional Newtonian potential. On a large scale, the corrections to the four-dimensional Newtonian potential can be ignored. While on a small scale, the correction from the volcano-like potential is more pronounced than the other two cases. Combining the specific corrections to the four-dimensional Newtonian potential of these three cases and the latest results of short-range gravity experiments, we get the constraint on the scale parameter as $$k > rsim 10^{-4}$$ k ≳ 10 - 4 eV, and constraint on the corresponding five-dimensional fundamental scale as $$M_* > rsim 10^5$$ M ∗ ≳ 10 5 TeV.

Do equidistant energy levels necessitate a harmonic potential?

Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only yields energy levels in a finite range and with a nonzero uncertainty. Within this study we review isospectral potentials from the literature and investigate the applicability of the harmonic oscillator hypothesis to recent measurements. First, we describe experimental results from literature by a harmonic oscillator model, obtaining a realistic size and depth of the resulting quantum well. Second, we use the shift-operator approach to calculate anharmonic non-polynomial potentials producing (partly) equidistant spectra. We discuss different potential types and interpret the possible modeling applications. Finally, by applying nth order perturbation theory we show that exactly equidistant eigenenergies cannot be achieved by polynomial potentials, except by the harmonic oscillator potential. In summary, we aim to give an overview over which conclusions may be drawn from the experimental determination of energy levels and which may not.

Relativistic Treatment of Quantum Mechanical Gravitational-Harmonic Oscillator Potential

The solutions of the Klein- Gordon equation for the quantum mechanical gravitational plus harmonic oscillator potential with equal scalar and vector potential have been presented using the parametric Nikiforov-Uvarov method. The energy eigenvalues were obtained in relativistic and non-relativistic regime and the corresponding un-normalized eigenfunctions in terms of Laguerre polynomials. The numerical values for the S – wave bound state were obtained.

Do Equidistant Energy Levels Necessitate a Harmonic Potential?

Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only yields energy levels in a finite range and with a nonzero uncertainty. Within this study we review isospectral potentials from the literature and investigate the applicability of the harmonic oscillator hypothesis to recent measurements. First, we describe experimental results from literature by a harmonic oscillator model, obtaining a realistic size and depth of the resulting quantum well. Second, we use the shift-operator approach to calculate anharmonic non-polynomial potentials producing (partly) equidistant spectra. We discuss different potential types and interpret the possible modeling applications. Finally, by applying n th o rder perturbation theory we show that exactly equidistant eigenenergies cannot be achieved by polynomial potentials, except by the harmonic oscillator potential. In summary, we aim to give an overview over which conclusions may be drawn from the experimental determination of energy levels and which may not.

Stability analysis of an ensemble of simple harmonic oscillators

In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to variations of the parameters, viz. the mass, temperature and the frequency of oscillators. Here, we introduce the Hessian matrix of the partition function as the model embedding function from the space of parameters to the set of real numbers. In this framework, we classify the regions in the parameter space of the harmonic oscillator fluctuations where they yield a stable statistical configuration. The mechanism of stability follows from the notion of the fluctuation theory. In Secs. ?? and ??, we provide the nature of local and global correlations and stability regions where the system yields a stable or unstable statistical basis, or it undergoes into geometric phase transitions. Finally, in Sec. ??, the comparison of results is provided with reference to other existing research.