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Supersymmetric Theory of Stochastics:Demystification of Self-Organized Criticality
Published in Christos H. Skiadas, Charilaos Skiadas, Handbook of Applications of Chaos Theory, 2017
Up to the overall factor, T, operator H^u is the Hamiltonian of the N=2 supersymmetric quantum mechanics. It is Hermitian and its spectrum is real and nonnegative. This implies that topological supersymmetry is never broken in this class of models as long as we believe that there must always exist the d^-symmetric ground state of the TE (see discussion at the end of Section 17.4.2).*
On the solutions and applications of the generalised Cornell potential
Published in Molecular Physics, 2022
Vinod Kumar, S. B. Bhardwaj, Ram Mehar Singh, Fakir Chand
In case of the diatomic molecules, the potential model generally includes some important parameters like the dissociation energy (), equilibrium bond length (), screening parameters (α) and inter-atomic separation (r). In past, many authors have investigated analytical and numerical solutions to the SE by using different potentials within the framework of a variety of methods like the Nikiforov–Uvarov (NU) method [9–12], asymptotic iteration method (AIM) [13–15], super symmetric quantum mechanics (SUSYQM) [16,17], exact quantisation rule (EQR) [18,19], parametric NU method (pNU) [20,21], Lie algebraic approach [22], NU functional analysis method (NUFA) [23–25], shifted 1/N expansion method [26], supersymmetric quantum mechanics (SUSYQM) [27], transformation-group method [28], etc. The Kratzer [29] and the pseudo harmonic [30] potentials are very important potentials as these find extensive applications in many areas of physics. Many authors have carried out important studies on energy eigenvalue spectra of diatomic molecules and mass spectra of mesons by exploring different potential models. A brief account of some important studies related to energy eigenvalue spectra of diatomic molecules and mass spectra of mesons is as follows.
Eigen solutions of the Schrodinger equation with variable mass under the influence of the linear combination of modified Woods–Saxon and Eckart potentials in toroidal coordinate
Published in Molecular Physics, 2020
A. Suparmi, C. Cari, Suci Faniandari
The analytical solution of the Schrodinger equation with variable mass was obtained using the linear combination of modified Woods–Saxon and Eckart potentials in toroidal coordinate. The energy spectra and wave function were solved using the Supersymmetric Quantum Mechanics method (SUSY QM). It showed that the energy value depends on the quantum numbers, the parameters of potentials, and variable separation constants. The quantum numbers had the most significant influence on the change in energy eigenvalue of molecule 59Co, 144Nd, and 209Bi, then followed by the potential parameters and the variable separation constant. The un-normalised ground state wave function was defined by operating the lowering and raising operator.
Study of Bohr–Mottelson with minimal length effect for Q-deformed modified Eckart potential and Bohr–Mottelson with Q-deformed quantum for three-dimensional harmonic oscillator potential
Published in Molecular Physics, 2020
A. Suparmi, C. Cari, M. Ma’arif
The Bohr–Mottelson Hamiltonian describes the nucleus models with two internal variables and , and three Euler angles . The corresponds to a nucleus deformation radially and corresponds to symmetric angle [3,4]. called as the axially symmetric case [2,5] corresponds to the prolate deformed nucleus [6] and occurs in the rigid deformed nucleus [3,5]. is the triaxial symmetric case and corresponds to the oblate [6]. The three Euler angles show the angles of nucleus in the collective model of Bohr–Mottelson Hamiltonian. The model solution of Bohr–Mottelson Hamiltonian that is called E(5) refers to the second-order phase transition between spherical and -unstable nuclei [7], X(5) corresponds to the first-order phase transition between spherical and prolate deformed nuclei [3], Z(5) corresponds to the transition from prolate to oblate shape [6] and Y(5) corresponds to the shape phase transition from the axial rotor to triaxial rotor [8]. In 2011, the Bohr–Mottelson Hamiltonian has been investigated by Bonatsos et al. with Davidson potential for axial symmetric [4]. The next years, the Bohr–Mottelson Hamiltonian has been solved including the Eckart potential [3], Kratzer potential [9] and Hulthen plus ring shape potential [1]. The methods that are used to solve Bohr–Mottelson Hamiltonian are asymptotic iteration method [1], Nikiforov–Uvarov [3] and supersymmetric quantum mechanics method [4].