Supersymmetric Method for Constructing Quasi-Exactly and Conditionally-Exactly Solvable Potentials
نویسندگان
چکیده
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.
منابع مشابه
Supersymmetric Method for Constructing Quasi-exactly Solvable Potentials
We propose a new method for constructing the quasi-exactly solvable (QES) potentials with two known eigenstates using supersymmetric quantum mechanics. General expression for QES potentials with explicitly known energy levels and wave functions of ground state and excited state are obtained. Examples of new QES potentials are considered.
متن کاملConditionally 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 کاملConditionally exactly solvable potentials and supersymmetric transformations
A general procedure is presented to construct conditionally exactly solvable (CES) potentials using the techniques of supersymmetric quantum mechanics. The method is illustrated with potentials related to the harmonic oscillator problem. Besides recovering known results, new CES potentials are also obtained within the framework of this general approach. The conditions under which this method le...
متن کاملA 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 کاملSupersymmetric Construction of Exactly Solvable Potentials and Non-linear Algebras
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 t...
متن کامل