Related papers: Quantum anharmonic oscillator and quasi-exactly so…
For quasiexactly solvable (QES) potentials a certain number of wave functions and energy levels can be analytically calculated. The complexity of an explicit calculation of the energy levels grows with the dimension of the QES sector. For a…
The method of q-oscillator lattices, proposed recently in [hep-th/0509181], provides the tool for a construction of various integrable models of quantum mechanics in 2+1 dimensional space-time. In contrast to any one dimensional quantum…
The model Hamiltonian of a two-dimensional Bose liquid (proposed earlier by Kane, Kivelson, Lee and Zhang as the Hamiltonian which has Jastrow-type wavefunctions as the ground-state solution), is shown to possess nonrelativistic…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives…
We present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively. We solve these models exactly via the functional Bethe ansatz method. For each case, we give closed-form solutions…
An Exactly-Solvable (ES) potential on the sphere $S^n$ is reviewed and the related Quasi-Exactly-Solvable (QES) potential is found and studied. Mapping the sphere to a simplex it is found that the metric (of constant curvature) is in…
We analyze the spectrum of the 3-site Bose-Hubbard model with periodic boundary conditions using a semiclassical method. The Bohr-Sommerfeld quantization is applied to an effective classical Hamiltonian which we derive using resonance…
A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator. This raises the question where the usual algebraic argument --…
We present a general procedure for determining possible (nonuniform) magnetic fields such that the Pauli equation becomes quasi-exactly solvable (QES) with an underlying $sl(2)$ symmetry. This procedure makes full use of the close…
We show that a polynomial H(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice…
We obtain the superfluid hydrodynamic equations of a multi-component Bose gas with short-ranged interactions at zero temperature under the local equilibrium assumption and show that the quantum pressure is generally present in the…
We show that for a particular model, the quantum mechanical bootstrap is capable of finding exact results. We consider a solvable system with Hamiltonian $H=SZ(1-Z)S$, where $Z$ and $S$ satisfy canonical commutation relations. While this…
Exact solvability (typically, of harmonic oscillators) in quantum mechanics usually implies an elementary form of the spectrum while in all the "next-to-solvable" models, the energies E are only available in an implicit form (typically, as…
The O(N) invariant quartic anharmonic oscillator is shown to be exactly solvable if the interaction parameter satisfies special conditions. The problem is directly related to that of a quantum double well anharmonic oscillator in an…
From the algebraic treatment of the quasi-solvable systems, and a q-deformation of the associated $su(2)$ algebra, we obtain exact solutions for the q-deformed Schrodinger equation with a 3-dimensional q-deformed harmonic oscillator…
The characterization of excitations in disordered quantum systems is a central issue in connection with glass physics and many-body localization. Here, we show that quench spectroscopy of a disordered model, as realized from its…
We extend the exactly solvable Hamiltonian describing $f$ quantum oscillators considered recently by J. Dorignac et al. by means of a new interaction which we choose as quasi exactly solvable. The properties of the spectrum of this new…
A quantum-field approach to studying the Bose systems at finite temperatures and in states with spontaneously broken symmetry, in particular in a superfluid state, is proposed. A generalized model of a self-consistent field (SCF) for…
The dynamics of a quantum anharmonic oscillator whose position is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential is studied. The (non-exponential) decoherence induced on the oscillator by the…