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Exact Solution for Two -Interacting Bosons on a Ring in the Presence of a -Barrier: Asymmetric Bethe Ansatz for Spatially Odd States
Maxim Olshanii, Mathias Albert, Gianni Aupetit-Diallo +2
In this article, we apply the recently proposed Asymmetric Bethe Ansatz method to the problem of two one-dimensional, short-range-interacting bosons on a ring in the presence of a…
Degeneracies In a Weighted Sum of Two Squares
Ishan Vinayagam Ramesh, Maxim Olshanii
This work is an attempt to classify and quantify instances when a weighted sum of two squares of positive integers, , can be realized in more than one way. Our pr…
Asymmetric Bethe Ansatz
Steven G. Jackson, Hélène Perrin, Gregory E. Astrakharchik +1
The recently proposed exact quantum solution for two -function-interacting particles with a mass-ratio in a hard-wall box [Y. Liu, F. Qi, Y. Zhang and S. Chen, iScienc…
A Novel Potential Featuring Off-Center Circular Orbits
Maxim Olshanii
In Book 1, Proposition 7, Problem 2 of his 1687 Philosophiae Naturalis Principia Mathematica, Isaac Newton poses and answers the following question: Let the orbit of a particle mov…
Exactly solvable quantum few-body systems associated with the symmetries of the three-dimensional and four-dimensional icosahedra
T. Scoquart, J. J. Seaward, S. G. Jackson +1
The purpose of this article is to demonstrate that non-crystallographic reflection groups can be used to build new solvable quantum particle systems. We explicitly construct a one-…
An exactly solvable quantum four-body problem associated with the symmetries of an octacube
Maxim Olshanii, Steven G. Jackson
In this article, we show that eigenenergies and eigenstates of a system consisting of four one-dimensional hard-core particles with masses , , , and in a hard-wall…
Supersymmetric Quantum Mechanics and Solitons of the sine-Gordon and Nonlinear Schrödinger Equations
Andrew Koller, Maxim Olshanii
We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSY--QM), reflectionless scattering, and soliton solutions of integrable partial different…