Nonlinear Supersymmetric (Darboux) Covariance of the Ermakov-Milne-Pinney Equation
M. V. Ioffe, H. J. Korsch
Abstract
It is shown that the nonlinear Ermakov-Milne-Pinney equation ρ+v(x)ρ=a/ρ3 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.
Create a lesson
Related papers
Phase transitions in non-Hermitian spherical integrals
Pierre Bousseyroux, Marc Potters
Factorization method for a clamped obstacle from near-field measurements via a far-field transformation
General Ozochiawaeze, Isaac Harris
Asymmetric phase transitions in random noncommutative geometries
Benedek Bukor, Masoud Khalkhali, Samuel Kováčik et al.
A Cumulative Framework for Solid Deformation
Lev Steinberg
Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components
Giorgio Gubbiotti, Lambertus Van Geemen, Pierandrea Vergallo
Reconstructability of Inverse Problems under Symmetry: Separating Structural, Effective, and Physical Upper Bounds
Isshin Arai