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Search Results: 1 - 10 of 6884 matches for " supersymmetric quantum mechanics. "
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Supersymmetric Quantum Mechanics and Painlevé IV Equation
David Bermúdez,David J. Fernández C.
Symmetry, Integrability and Geometry : Methods and Applications , 2011,
Abstract: As it has been proven, the determination of general one-dimensional Schr dinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlevé IV equation. Finally, we classify these solutions into three relevant hierarchies.
On Solvable Potentials, Supersymmetry, and the One-Dimensional Hydrogen Atom  [PDF]
R. P. Martínez-y-Romero, H. N. Núnez-Yépez, A. L. Salas-Brito
Communications and Network (CN) , 2010, DOI: 10.4236/cn.2010.21009
Abstract: The ways for improving on techniques for finding new solvable potentials based on supersymmetry and shape invariance has been discussed by Morales et al. [1] In doing so they address the peculiar system known as the one-dimensional hydrogen atom. In this paper we show that their remarks on such problem are mistaken. We do this by explicitly constructing both the one-dimensional Coulomb potential and the superpotential associated with the problem, objects whose existence are denied in the mentioned paper.
Novel Superpotentials for Supersymmetric Quantum Mechanics: A New Mathematical Investigation and Study  [PDF]
Alireza Heidari, Seyedali Vedad, Mohammadali Ghorbani
Journal of Modern Physics (JMP) , 2012, DOI: 10.4236/jmp.2012.34043
Abstract: The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the authors’ name: Alireza Heidari and Seyedali Vedad. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.4 304-311, 2012, has been removed from this site.
Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators
Alonso Contreras-Astorga,David J. Fernández C.,Javier Negro
Symmetry, Integrability and Geometry : Methods and Applications , 2012,
Abstract: The intertwining technique has been widely used to study the Schr dinger equation and to generate new Hamiltonians with known spectra. This technique can be adapted to find the bound states of certain Dirac Hamiltonians. In this paper the system to be solved is a relativistic particle placed in a magnetic field with cylindrical symmetry whose intensity decreases as the distance to the symmetry axis grows and its field lines are parallel to the x y plane. It will be shown that the Hamiltonian under study turns out to be shape invariant.
Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
Alexander A. Andrianov,Andrey V. Sokolov
Symmetry, Integrability and Geometry : Methods and Applications , 2009,
Abstract: When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples.
A New Class of Exactly Solvable Models within the Schrödinger Equation with Position Dependent Mass  [PDF]
Anis Dhahbi, Yassine Chargui, Adel Trablesi
Journal of Applied Mathematics and Physics (JAMP) , 2019, DOI: 10.4236/jamp.2019.75068
Abstract: The study of physical systems endowed with a position-dependent mass (PDM) remains a fundamental issue of quantum mechanics. In this paper we use a new approach, recently developed by us for building the quantum kinetic energy operator (KEO) within the Schrodinger equation, in order to construct a new class of exactly solvable models with a position varying mass, presenting a harmonic-oscillator-like spectrum. To do so we utilize the formalism of supersymmetric quantum mechanics (SUSY QM) along with the shape invariance condition. Recent outcomes of non-Hermitian quantum mechanics are also taken into account.
Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2

Dong Kun,Tian Gui-Hua,Sun Yue,

中国物理 B , 2011,
Singular Isotonic Oscillator, Supersymmetry and Superintegrability
Ian Marquette
Symmetry, Integrability and Geometry : Methods and Applications , 2012,
Abstract: In the case of a one-dimensional nonsingular Hamiltonian H and a singular supersymmetric partner H_a, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown how we can construct an adequate partner by using infinite barriers placed where are located the singularities on the real axis and recover isospectrality. This method was applied to superpartners of the harmonic oscillator with one singularity. In this paper, we apply this method to the singular isotonic oscillator with two singularities on the real axis. We also applied these results to four 2D superintegrable systems with second and third-order integrals of motion obtained by Gravel for which polynomial algebras approach does not allow to obtain the energy spectrum of square integrable wavefunctions. We obtain solutions involving parabolic cylinder functions.
Generalized Deformed Commutation Relations with Nonzero Minimal Uncertainties in Position and/or Momentum and Applications to Quantum Mechanics
Christiane Quesne,Volodymyr M. Tkachuk
Symmetry, Integrability and Geometry : Methods and Applications , 2007,
Abstract: Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and momentum are determined and the effect on the energy spectrum and eigenfunctions of the harmonic oscillator in an electric field is studied. The second extension is a function-dependent generalization of the simplest quadratic commutation relation with only a nonzero minimal uncertainty in position. Such an uncertainty now becomes dependent on the average position. With each function-dependent commutation relation we associate a family of potentials whose spectrum can be exactly determined through supersymmetric quantum mechanical and shape invariance techniques. Some representations of the generalized Heisenberg algebras are proposed in terms of conventional position and momentum operators $x$, $p$. The resulting Hamiltonians contain a contribution proportional to $p^4$ and their $p$-dependent terms may also be functions of $x$. The theory is illustrated by considering P schl-Teller and Morse potentials.
Harmonic Oscillator SUSY Partners and Evolution Loops
David J. Fernández
Symmetry, Integrability and Geometry : Methods and Applications , 2012,
Abstract: Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric phases will be as well studied.
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