Nonlinear supersymmetric (Darboux) covariance of the Ermakov–Milne–Pinney equation
| Autor: | M.V Ioffe, Hans Jürgen Korsch |
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| Rok vydání: | 2003 |
| Předmět: |
Nonlinear Sciences - Exactly Solvable and Integrable Systems
FOS: Physical sciences General Physics and Astronomy Order (ring theory) Mathematical Physics (math-ph) General Relativity and Quantum Cosmology (gr-qc) Function (mathematics) Covariance Particle in a box General Relativity and Quantum Cosmology Prime (order theory) Nonlinear system Bound state Exactly Solvable and Integrable Systems (nlin.SI) Invariant (mathematics) Mathematical Physics Mathematics Mathematical physics |
| Zdroj: | Physics Letters A. 311:200-205 |
| ISSN: | 0375-9601 |
| DOI: | 10.1016/s0375-9601(03)00495-x |
| Popis: | It is shown that the nonlinear Ermakov-Milne-Pinney equation $\rho^{\prime\prime}+v(x)\rho=a/\rho^3$ obeys the property of covariance under a class of transformations of its coefficient function. This property is derived by using supersymmetric, or Darboux, transformations. The general solution of the transformed equation is expressed in terms of the solution of the original one. Both iterations of these transformations and irreducible transformations of second order in derivatives are considered to obtain the chain of mutually related Ermakov-Milne-Pinney equations. The behaviour of the Lewis invariant and the quantum number function for bound states is investigated. This construction is illustrated by the simple example of an infinite square well. Comment: 8 pages |
| Databáze: | OpenAIRE |
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