Related papers: Do equidistant energy levels necessitate a harmoni…
We investigate the spectroscopy and decays of the charmonium and upsilon systems in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections and the…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
In a recent thermodynamic analysis of the harmonic oscillator and using an interpolation procedure, Boyer has shown that the existence of a zero-point energy leads to the Planck spectrum. Here we avoid the interpolation by adding a…
The spectral potential is the dynamical generalization of the Kohn-Sham potential. It targets, in principle exactly, the spectral function in addition to the electronic density. Here we examine the spectral potential in one of the simplest…
Rydberg atoms and beams of ultracold polar molecules have become highly useful experimental tools in recent years. There is therefore a need for accessible calculations of interaction potentials between such particles and nearby surfaces…
The dynamical law obeyed by the one-dimensional physical systems in the scale relativity approach is reduced to a Riccati nonlinear differential equation. Applied to the harmonic oscillator potential, we show that such an approach permits…
A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice $\mathbb{Z}^d$ is considered. The anharmonic potential is of general type, which in particular means that it…
We investigate the nonrelativistic magnetic effect on the energy spectra, expectation values of some quantum mechanical observables and diamagnetic susceptibility for some diatomic molecules bounded by the Isotropic oscillator plus inverse…
We consider the energy spectrum $\Xi_E(N)$ of harmonic maps from the sphere into a closed Riemannian manifold $N$. While a well known conjecture asserts that $\Xi_E(N)$ is discrete whenever $N$ is analytic, for most analytic targets it is…
The de Haas - van Alphen effect in quasi-two-dimensional metals is studied at arbitrary parameters. The oscillations of the chemical potential may substantially change the temperature dependence of harmonic amplitudes that is usually used…
Equilibrium thermodynamic laws are typically applied to horizons in general relativity without stating the conditions that bring them into equilibrium. We fill this gap by applying a new thermodynamic interpretation to a generalized…
We obtain the analytical solutions to the Schr\"odinger equation for the attractive inverse-square potential in an induced electric dipole moment system under the influence of the harmonic oscillator. We show that bound states can exist…
The Quasi-harmonic (QH) approximation uses harmonic vibrational frequencies omega(H,Q,V), computed at volumes V near the volume where the Born-Oppenheimer (BO) energy is minimum. When this is used in the harmonic free energy, QH…
A generalized harmonic oscillator on noncommutative spaces is considered. Dynamical symmetries and physical equivalence of noncommutative systems with the same energy spectrum are investigated and discussed. General solutions of…
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic…
We develop performance criteria for the objective comparison of different classes of single-degree-of-freedom oscillators under stochastic excitation. For each family of oscillators, these objective criteria take into account the maximum…
In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as…
A very simple procedure to calculate eigenenergies of quantum anharmonic oscillators is presented. The method, exact but for numerical computations, consists merely in requiring the vanishing of the Wronskian of two solutions which are…
This simple text considers an application of Bohr-Sommerfeld quantization rule. It might be of interest for the students of physics.
The study of the convergence of power series expansions of energy eigenvalues for anharmonic oscillators in quantum mechanics differs from general understanding, in the case of quasi-exactly solvable potentials. They provide examples of…