Related papers: Exactly separable version of the Bohr Hamiltonian …
An analytical solution for the Davydov-Chaban Hamiltonian with a sextic oscillator potential for the variable $\beta$ and $\gamma$ fixed to $30^{\circ}$, is proposed. The model is conventionally called Z(4)-Sextic. For the considered…
The Deformation Dependent Mass (DDM) Kratzer model is constructed by considering the Kratzer potential in a Bohr Hamiltonian, in which the mass is allowed to depend on the nuclear deformation, and solving it by using techniques of…
From the semi-empirical formalisms of Bohr-Mottelson, a new model, based on the effect of beta- and gamma- head energies and the variable moment of inertia, was developed to calculate the ground state rotational band of almost all deformed…
An exact boson mapping of the reduced BCS (equal strength) pairing Hamiltonian is considered. In the mapping, fermion pair operators are mapped exactly to the corresponding bosons. The image of the mapping results in a Bose-Hubbard model…
Analytical expressions of the wave functions are derived for a Bohr Hamiltonian with the Manning{Rosen potential in the cases of {\gamma}-unstable nuclei and axially symmetric prolate deformed ones with {\gamma}=0. By exploiting the results…
A prolate $\gamma$-rigid version of the Bohr-Mottelson Hamiltonian with a quartic anharmonic oscillator potential in $\beta$ collective shape variable is used to describe the spectra for a variety of vibrational-like nuclei. Speculating the…
With a number of special Hamiltonians, solutions of the Schr\"{o}dinger equation may be found by separation of variables in more than one coordinate system. The class of potentials involved includes a number of important examples, including…
The equation of the Bohr-Mottelson Hamiltonian with a sextic oscillator potential is solved for $\gamma$-rigid prolate nuclei. The associated shape phase space is reduced to three variables which are exactly separated. The angular equation…
Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. In the variational quantum eigensolver, a decomposition of the target Hamiltonian into exactly solvable fragments can be used for…
We present a family of exactly solvable models at arbitrary filling in any dimensions which exhibit novel superconductivity with interband pairing. By the use of the hidden $SU(2)$ algebra the Hamiltonians were diagonalized explicitly. The…
Recently, a variant of the Bohr Hamiltonian was proposed where the mass term is allowed to depend on the beta variable of nuclear deformation. Analytic solutions of this modified Hamiltonian have been obtained using the Davidson and the…
In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting…
In a recent work [1] we presented results for the Bose-Fermi-Hubbard model (BFHM) in the limit of ultrafast fermions. The present work gives an overview over the used methods and an deeper insight into the implications arising from the…
The conventional Hamiltonian $H= p^2+ V_N(x)$, where the potential $V_N(x)$ is a polynomial of degree $N$, has been studied intensively since the birth of quantum mechanics. In some cases, its spectrum can be determined by combining the WKB…
An analytic, parameter-free (up to overall scale factors) solution of the Bohr Hamiltonian involving axially symmetric quadrupole and octupole deformations, as well as an infinite well potential, is obtained, after separating variables in a…
A systematic analysis of low-lying quadrupole and octupole collective states is presented, based on the microscopic energy density functional framework. By mapping the deformation constrained self-consistent axially symmetric mean-field…
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…
We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
We calculate the eigenvalues and their corresponding eigenfunctions of the Bohrs collective Hamiltonian with the help of the modified Poschl-Teller potential model within -unstable structure. Our numerical results for the ground state beta…