Related papers: The quantum double well anharmonic oscillator in a…
The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave…
We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement schemes. Detection probability has…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
A family of quantum anharmonic oscillators is studied in any finite spatial dimension in the scheme of first quantization and the investigation of their eigenenergies is presented. The statistical properties of the calculated eigenenergies…
We study the anharmonic double well in quantum mechanics using exact Wentzel-Kramers-Brillouin (WKB) methods in a 't Hooft-like double scaling limit where classical behavior is expected to dominate. We compute the tunneling action in this…
A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical anharmonic oscillator and the double-well potential given by $V= m^2 x^2+g x^4$ at arbitrary $g \geq 0$ for…
We perform a study of various anharmonic potentials using a recently developed method. We calculate both the wave functions and the energy eigenvalues for the ground and first excited states of the quartic, sextic and octic potentials with…
The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale. By using a perturbative approach, we analytically…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
We obtain tight upper and lower bounds to the eigenvalues of an anharmonic oscillator with a rational potential. We compare our bounds with results given by other approaches.
In multifrequency atomic force microscopy higher eigenmodes are externally excited to enhance resolution and contrast while simultaneously increasing the number of experimental observables with the use of gentle forces. Here, the…
Today it still remains a challenge whether quantum mechanics has an underlying statistical explanation or not. While there are and were a lot of models trying to explain quantum phenomena with statistical methods these all failed on certain…
We study the effect of anharmonicity in quantum anharmonic oscillators, by computing the energy gap between the ground and the 1st excited state using the numerical bootstrap method. Based on perturbative formulae of limiting coupling…
A quantum anharmonic oscillator is defined by the Hamiltonian ${\cal H}= -\frac{ {\rm d^{2}}}{{\rm d}x^{2}} + V(x)$, where the potential is given by $V(x) = \sum_{i=1}^{m} c_{i} x^{2i}$ with $c_{m}>0$. Using the Sinc collocation method…
We study the asymptotic behavior of the spectrum of a quantum system which is a perturbation of a spherically symmetric anharmonic oscillator in dimension 2. We prove that a large part of its eigenvalues can be obtained by Bohr-Sommerfeld…
Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…
In this note we consider a one-dimensional quantum mechanical particle constrained by a parabolic well perturbed by a Gaussian potential. As the related Birman-Schwinger operator is trace class, the Fredholm determinant can be exploited in…
A simple method for the calculation of higher orders of the logarithmic perturbation theory for bound states of the spherical anharmonic oscillator is developed. The structure of the perturbation series for energy eigenvalues of the sextic…
This work is mainly based on some theoretical surveys on two dimensional quantum gravitational well, considering harmonic oscillator potential causes an effective plank constant. We find that there is a similarity between two different…