Related papers: From quartic anharmonic oscillator to double well potential

From quartic anharmonic oscillator to double well potential

URL: http://arxiv.org/abs/2111.01546v2
Date: Thu, 30 Dec 2021 22:04:45 GMT
Title: From quartic anharmonic oscillator to double well potential
Authors: Alexander V. Turbiner, J.C. del Valle
Abstract summary: It is shown that by taking uniformly-accurate approximation for anharmonic oscillator eigenfunction $Psi_ao(u)$, obtained recently, it is possible to get highly accurate approximation for both the eigenfunctions of the double-well potential and its eigenvalues.
Score: 77.34726150561087
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: It is already known that the quantum quartic single-well anharmonic oscillator $V_{ao}(x)=x^2+g^2 x^4$ and double-well anharmonic oscillator $V_{dw}(x)= x^2(1 - gx)^2$ are essentially one-parametric, their eigenstates depend on a combination $(g^2 \hbar)$. Hence, these problems are reduced to study the potentials $V_{ao}=u^2+u^4$ and $V_{dw}=u^2(1-u)^2$, respectively. It is shown that by taking uniformly-accurate approximation for anharmonic oscillator eigenfunction $\Psi_{ao}(u)$, obtained recently, see JPA 54 (2021) 295204 [1] and Arxiv 2102.04623 [2], and then forming the function $\Psi_{dw}(u)=\Psi_{ao}(u) \pm \Psi_{ao}(u-1)$ allows to get the highly accurate approximation for both the eigenfunctions of the double-well potential and its eigenvalues.

Related papers

An analogue of the Pöschl-Teller anharmonic oscillator on an $N$-dimensional sphere [0.0]
A Schr"odinger particle on an $N$-dimensional ($Ngeqslant2$) hypersphere of radius $R$ is considered. The particle is subjected to the action of a force characterized by the potential $V(theta)=2momega_12R2tan2(theta/2)+2momega_22R2cot2(theta/2)$, where $0leqslantthetaleqslantpi$ is
arXiv Detail & Related papers (2024-08-20T13:51:45Z)
A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
arXiv Detail & Related papers (2023-09-25T17:54:19Z)
Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
arXiv Detail & Related papers (2023-06-21T10:11:28Z)
Exactly solvable piecewise analytic double well potential $V_{D}(x)=min[(x+d)^2,(x-d)^2]$ and its dual single well potential $V_{S}(x)=max[(x+d)^2,(x-d)^2]$ [0.0]
Two piecewise analytic quantum systems with a free parameter $d>0$ are obtained. Their eigenvalues $E$ for the even and odd parity sectors are determined. vivid pictures unfold showing the tunneling effects between the two wells.
arXiv Detail & Related papers (2022-09-20T03:46:03Z)
On parametric resonance in the laser action [91.3755431537592]
We consider the selfconsistent semiclassical Maxwell--Schr"odinger system for the solid state laser. We introduce the corresponding Poincar'e map $P$ and consider the differential $DP(Y0)$ at suitable stationary state $Y0$.
arXiv Detail & Related papers (2022-08-22T09:43:57Z)
Near-optimal fitting of ellipsoids to random points [68.12685213894112]
A basic problem of fitting an ellipsoid to random points has connections to low-rank matrix decompositions, independent component analysis, and principal component analysis. We resolve this conjecture up to logarithmic factors by constructing a fitting ellipsoid for some $n = Omega(, d2/mathrmpolylog(d),)$. Our proof demonstrates feasibility of the least squares construction of Saunderson et al. using a convenient decomposition of a certain non-standard random matrix.
arXiv Detail & Related papers (2022-08-19T18:00:34Z)
Dynamics of Non-Gaussian Entanglement of Two Magnetically Coupled Modes [0.0]
This paper surveys the quantum entanglement of two coupled harmonic oscillators via angular momentum. We study the effect of the anisotropy $ R=omega_12/omega_22 $, $omega_c$, asymmetry $ |n-m| $ and dynamics on the entanglement.
arXiv Detail & Related papers (2021-08-09T15:52:34Z)
Anharmonic oscillator: a solution [77.34726150561087]
The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
arXiv Detail & Related papers (2020-11-29T22:13:08Z)
On the four-body problem in the Born-Oppenheimer approximation [0.0]
The model allows exact solvability and a critical analysis of the Born-Oppenheimer approximation. It is shown that the sum of the first two terms of the Puiseux series, in powers of the dimensionless parameter $sigma=fracmM$, coincide exactly with the values obtained in the Born-Oppenheimer approximation.
arXiv Detail & Related papers (2020-07-29T16:43:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.