Supersymmetric Construction of Exactly Solvable Potentials and Non-linear Algebras
نویسندگان
چکیده
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 help 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 non-linear algebra which is of quadratic and cubic type for the SUSY partners of the linear and radial harmonic oscillator, respectively.
منابع مشابه
Conditionally exactly solvable potentials: A supersymmetric construction method
We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of one-dimensional potentials are constructed whose corresponding Schrödinger eigenvalue problem can be solved exactly under certain conditions of the potential paramete...
متن کاملNon-linear coherent states associated with conditionally exactly solvable problems
Recently, based on a supersymmetric approach, new classes of conditionally exactly solvable problems have been found, which exhibit a symmetry structure characterized by non-linear algebras. In this paper the associated “nonlinear” coherent states are constructed and some of their properties are discussed in detail. PACS numbers: 03.65.Fd, 02.20.Qs, 42.50.-p
متن کاملMultichannel coupling with supersymmetric quantum mechanics and exactly-solvable model for Feshbach resonance
Abstract A new type of supersymmetric transformations of the coupled-channel radial Schrödinger equation is introduced, which do not conserve the vanishing behavior of solutions at the origin. Contrary to usual transformations, these “non-conservative” transformations allow, in the presence of thresholds, the construction of potentials with coupled scattering matrices from uncoupled potentials....
متن کاملOn Solvable Potentials for One Dimensional Schrödinger and Fokker-Planck Equations
One construction of exactly-solvable potentials for Fokker-Planck equation is considered based on supersymmetric quantum mechanics approach. PACS numbers: 03.65.-w, 03.65.Ge, 03.65.Ca, 02.90.+p Submitted to Journal of Physics A: Mathematical and General
متن کاملSupersymmetric Method for Constructing Quasi-Exactly and Conditionally-Exactly Solvable Potentials
Using supersymmetric quantum mechanics we develop a new method for constructing quasi-exactly solvable (QES) potentials with two known eigenstates. This method is extended for constructing conditionally-exactly solvable potentials (CES). The considered QES potentials at certain values of parameters become exactly solvable and can be treated as CES ones.
متن کامل