Supersymmetric construction of exactly solvable potentials and nonlinear algebras
Georg Junker,Pinaki Roy +1 more
TLDR
Using algebraic tools of supersymmetric quantum mechanics, this article constructed classes of conditionally exactly solvable potentials, being the supersymmetric partners of the linear or radial harmonic oscillator.Abstract:
Using algebraic tools of supersymmetric quantum mechanics, we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the aid of the raising and lowering operators of these harmonic oscillators and the SUSY operators, we construct ladder operators for these new conditionally solvable systems. It is found that these ladder operators, together with the Hamilton operator, form a nonlinear algebra, which is of the quadratic and cubic types for the SUSY partners of the linear and radial harmonic oscillators, respectively.read more
Citations
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Conditionally Exactly Solvable Potentials: A Supersymmetric Construction Method☆
Georg Junker,Pinaki Roy +1 more
TL;DR: In this paper, a general method for the construction of conditionally exactly solvable potentials is presented, based on algebraic tools known from supersymmetric quantum mechanics, whose corresponding Schrodinger eigenvalue problem can be solved exactly under certain conditions of the potential parameters.
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Higher-order SUSY, linearized nonlinear Heisenberg algebras and coherent states
TL;DR: Using an iterative construction of the first-order intertwining technique, this article found k-parametric families of exactly solvable anharmonic oscillators whose spectra consist of a part isospectral to the oscillator plus k additional levels at arbitrary positions below E0D 1.
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Nonlinear supersymmetry for spectral design in quantum mechanics
TL;DR: In this paper, a nonlinear (polynomial, N-fold) SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed, and the full classification of ladder-reducible and irreducibly chains of sUSY algebras in one-dimensional QM is given.
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Nonlinear supersymmetric quantum mechanics: concepts and realizations
TL;DR: The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed in this paper, its building from the chains (ladders) of linear SUSY systems is outlined and different one-dimensional and two-dimensional realizations are described.
Journal ArticleDOI
Exactly solvable hydrogen-like potentials and the factorization method
TL;DR: In this article, a set of factorization energies is introduced, giving rise to a generalization of the Schrodinger (or Infeld and Hull) factorization for the radial hydrogen-like Hamiltonian.
References
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Book
Generalized Coherent States and Their Applications
TL;DR: In this paper, the authors define the notion of generalized coherent states and define a generalization of the Coherent State Representation T?(g) of the Heisenberg-Weyl Group.
Book
Supersymmetric Methods in Quantum and Statistical Physics
TL;DR: In this article, the Witten model was used to solve the exact solution of quantum-mechanical Eigenvalue problems in classical stochastic dynamics and supersymmetry in the Pauli and Dirac Equations.