Related papers: Higher Order Supersymmetric Truncated Oscillators
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
We define Sturmian basis functions for the harmonic oscillator and investigate whether recent insights into Sturmians for Coulomb-like potentials can be extended to this important potential. We also treat many body problems such as coupling…
We apply power series expansion to symmetric multi-well oscillators bounded by two infinite walls. The spectrum and expectation values obtained are compared with available exact and approximate values for the unbounded ones. It is shown…
In recent years, progress toward the classification of superintegrable systems with higher order integrals of motion has been made. In particular, a complete classification of all exotic potentials with a third or a fourth order integrals,…
In this work the supersymmetric technique is applied to the truncated oscillator to generate Hamiltonians ruled by second and third-order polynomial Heisenberg algebras, which are connected to the Painlev\'e IV and Painlev\'e V equations…
We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal…
We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $\cal PT$ symmetry may…
We develop a framework for multiscale analysis of elliptic operators with high-contrast random coefficients. For a general class of such operators, we provide a detailed spectral analysis of the corresponding homogenised limit operator.…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
Coupled quantum harmonic oscillators, studied by many authors using many different techniques over the decades, are frequently used toy-models to study open quantum systems. In this manuscript, we explicitly study the simplest oscillator…
After a brief introduction recalling how, in the limit in which the mass and the electric charge of the electron and the positron tend to zero, Quantum Electrodynamics reduces to a collection of uncoupled quantum supersymmetric harmonic…
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even…
In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. It is illustrated through the particular cases of the harmonic oscillator and the Coulomb potential. In this kind of system the…
Central D-dimensional Hamiltonians $H = p^2 + a |\vec{r}|^2 + b |\vec{r}|^4 + >... + z |\vec{r}|^{4q+2}$ (where z=1) are considered in the limit $D \to \infty$ where numerical experiments revealed recently a new class of q-parametric…
In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting…
We discuss the diagonalization of a general Hamiltonian operator for a set of coupled harmonic oscillators and determine the conditions for the existence of bound states. We consider the particular cases of two and three oscillators studied…
We construct an N=2 supersymmetric extension of the Pais-Uhlenbeck oscillator for distinct frequencies of oscillation. A link to a set of decoupled N=2 supersymmetric harmonic oscillators with alternating sign in the Hamiltonian is…
Superoscillations are a phenomenon in physics, where linear combinations of low-frequency plane waves interfere almost destructively in such a way that the resulting wave has a higher frequency than any of the individual waves. The…
High-order harmonic generation (HHG) in aligned linear molecules can offer valuable information about strong-field interactions in lower-lying molecular orbitals, but extracting this information is difficult for three-dimensional molecular…