Related papers: Exactly solvable models of nuclei
We consider the Ricatti equation in the context of population dynamics, quantum scattering and a more general context. We examine some exactly solvable cases of real life interest.
The challenging nuclear many-body problem is discussed along with classifications and qualitative descriptions of existing methods and models. We present detailed derivations of a new method where cluster correlations co-exist with an…
By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable quantum potentials. We obtain, in this way, two new…
We present three classes of exactly solvable models for fermion and boson systems, based on the pairing interaction. These models are solvable in any dimension. As an example we show the first results for fermion interacting with repulsive…
A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian…
We discuss the application of a theory of large-amplitude collective motion to a simple model mimicking the pairing-plus-quadrupole model of nuclear physics.
We present a class of one-to-one matching models with perfectly transferable utility. We discuss identification and inference in these separable models, and we show how their comparative statics are readily analyzed.
The relevance of the pseudospin symmetry in nuclei is considered. New insight is obtained from looking at the continuous transition from a model satisfying the spin symmetry to another one satisfying the pseudospin symmetry. This study…
Following a brief reminder of how the pairing model can be solved exactly, we describe how this can be used to address two interesting issues in nuclear structure physics. One concerns the mechanism for realizing superconductivity in finite…
Coupled-cluster theory is a powerful tool for first-principles calculations of atomic nuclei, enabling accurate predictions of nuclear observables across the Segr\`e chart. While coupled-cluster computations are especially efficient at…
Nuclear pairing correlations are known to play an important role in various single-particle and collective aspects of nuclear structure. After the first idea by A. Bohr, B. Mottelson and D. Pines on similarity of nuclear pairing to electron…
Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…
We discuss a universal algebraic approach to quasi-exactly solvable models which allows us to interpret them as constrained Hamiltonian systems with a finite number of physical states. Using this approach we reproduce well-known…
We construct a quantum mechanical model of the Calogero type for the icosahedral group as the structural group. Exact solvability is proved and the spectrum is derived explicitly.
We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…
N=2 supersymmetric field theories in two dimensions have been extensively studied in the last few years. Many of their properties can be determined along the whole renormalization group flow, like their coupling dependence and soliton…
We present a unified treatment of exact solutions for a class of four quantum mechanical models, namely the singular anharmonic potential, the generalized quantum isotonic oscillator, the soft-core Coulomb potential, and the…
The exactly and quasi-exactly solvable problems for spin one-half in one dimension on the basis of a hidden dynamical symmetry algebra of Hamiltonian are discussed. We take the supergroup, $OSP(2|1)$, as such a symmetry. A number of exactly…
On example of tasks of class NP the questions concerning accuracy of work of already existing and possible in the future algorithms for the solution of tasks on discrete structures are considered.
We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new…