Related papers: Two-body quantum mechanical problem on spheres
We present the quantum mechanics of "partial-trace" non-linear sigma models, on the grounds of a fully symmetry-based procedure. After the general scheme is sketched, the particular example of a particle on the two-sphere is explicitly…
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These…
The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses because its discussion usually requires wavepackets built on the Airy functions -- a difficult computation. Here, on the…
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
The problem of $N$ particles interacting through pairwise central forces is notoriously intractable for $N\geq3$. Some quite remarkable specific cases have been solved in one dimension, whereas higher-dimensional exactly solved systems…
We consider the Kepler two-body problem in presence of the cosmological constant $\Lambda$. Contrary to the classical case, where finite solutions exist for any angular momentum of the system $L$, in presence of $\Lambda$ finite solutions…
The dominantly orbital state method allows a semiclassical description of quantum systems. At the origin, it was developed for two-body relativistic systems. Here, the method is extended to treat two-body Hamiltonians and systems with three…
We introduce an approach, based on the coordinate space Faddeev equations, to solve the quantum mechanical three-body Coulomb problem in the continuum. We apply the approach to compute measured properties of the first two $0^+$ levels in…
We derive analytic expressions for the two-body matrix elements in finite spherical quantum Hall systems in terms of a general scalar interaction expressed as a sum over Legendre polynomials, and we derive the corresponding pair…
We introduce a real-space version of the Bardeen-Cooper-Schrieffer interaction allowing the investigation of the non-trivial interplay between many-body physics and particles confinement on a quantum graph. When the two-body problem is…
We prove the existence of chaotic trajectories for the two body problem on a sphere. The trajectories we construct encounter near-collisions and are similar to the second species solutions of Poincar\'e of the classical 3 body problem. The…
We calculate exactly, using finite size techniques, the quantum mechanical and many-body effects to the self-capacitance of a spherical quantum dot in the regime of extreme confinement, where the radius of the sphere is much smaller than…
We consider a system of two identical fermions of general mass interacting with a third distinguishable particle via a contact interaction within an isotropic three-dimensional harmonic trap. We calculate time-dependent observables of the…
Solving the quantum-mechanical many-body problem requires scalable computational approaches, which are rooted in a good understanding of the physics of correlated electronic systems. Interacting electrons in a magnetic field display a huge…
We introduce the quantum mechanical formalism for treating surface plasmon polariton scattering at an interface. Our developed theory - which is fundamentally different from the analogous photonic scenario - is used to investigate the…
In this letter, I have considered one-dimensional quantum system with different masses $m$ and $M$, which does not appear integrable in general. However I have found an exact two-body wave function and due to the extension of the integrable…
In this article, we analyse an integral equation of the second kind that represents the solution of $N$ interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the…
Quantum interference lies at the heart of several surprising equilibrium and non-equilibrium phenomena in many-body Physics. Here we discuss two recently explored non-equilibrium scenarios where external periodic drive applied to closed…
We solve the problem of a dimer moving on a spherical surface and find that its binding energy and wave function are sensitive to the total angular momentum. The dimer gets squeezed in the direction orthogonal to the center-of-mass motion…