Related papers: Multiparticle SUSY quantum mechanics and the repre…
Supersymmetry (SUSY) provides elegant solutions to several problems in the Standard Model and searches for SUSY particles are an important component of the LHC physics program. The latest results from electroweak and strong SUSY searches…
New two-dimensional quantum model - the generalization of the Scarf II - is completely solved analytically for the integer values of parameter. This model being not amenable to conventional procedure of separation of variables is solved by…
Links between supersymmetric classical and quantum mechanics are explored. Diagrammatic representations for \hbar-expansions of norms of ground states are provided. The WKB spectra of supersymmetric non harmonic oscillators are found.
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
A nuclear physics example of the U(6/2) supersymmetry group is considered. It is shown that this group contains a supersymmetric subgroup with a structure similar to the SUSY model of the quantum field theory (QFT). A comparison of two…
Supersymmetry (SUSY) in quantum mechanics is extended from square-integrable states to those satisfying the outgoing-wave boundary condition, in a Klein-Gordon formulation. This boundary condition allows both the usual normal modes and…
Searches for supersymmetry (SUSY) often rely on a combination of hard physics objects (jets, leptons) along with large missing transverse energy to separate New Physics from Standard Model hard processes. We consider a class of…
Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each…
The quantization procedure for both N=1 and N=2 supersymmetric Korteweg-de Vries (SUSY KdV) hierarchies is constructed. Namely, the quantum counterparts of the monodromy matrices, built by means of the integrated vertex operators, are shown…
Supersymmetry (SUSY) relating bosons and fermions plays an important role in unifying different fundamental interactions in particle physics. Since no superpartners of elementary particles have been observed, SUSY, if present, must be…
In this paper we will report on a one-dimensional, non-separable quantum many-particle system introduced in [arXiv:1504.08283,arXiv:1604.06693]. It consists of two (distinguishable) particles moving on the half-line being subjected to two…
The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite…
The new approach to quantum mechanical problems is proposed. Quantum states are represented in an algebraic program, by lists of variable length, while operators are well defined functions on these lists. Complete numerical solution of a…
In this work the supersymmetric technique is applied to the truncated oscillator to generate Hamiltonians ruled by second and third-order polynomial Heisenberg algebras, which are connected to the Painlev\'e IV and Painlev\'e V equations…
The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same…
Some recent results in supersymmetric quantum mechanics are presented. New semi-classical approximation formulas for Witten's realization of supersymmetric quantum mechanics are discussed. Implications of the supersymmetric structure of…
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and…
Within the framework of second order derivative (one dimensional) SUSYQM we discuss particular realizations which incorporate large energy shifts between the lowest states of the spectrum of the superhamiltonian (of Schr\"odinger type). The…
We employ our new approach to non-relativistic supersymmetric quantum mechanics (SUSY-QM), (J. Phys. Chem. A 114, 8202(2010)) for any number of dimensions and distinguishable particles, to treat the hydrogen atom in full three-dimensional…