The transverse envelope of accelerating twisted Dirac states in nonuniform axial B and E fields obeys a Caldirola-Kanai Schrödinger equation whose solution is obtained by Ermakov mapping to a scaling function b(z) satisfying a generalized Pinney equation.
[25]; and (iii) an explicit construction of the Ermakov–Pinney solution from two linearly independent solutions of the associated Hill equation
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Effective Caldirola-Kanai Model for Accelerating Twisted Dirac States in Nonuniform Axial Fields
The transverse envelope of accelerating twisted Dirac states in nonuniform axial B and E fields obeys a Caldirola-Kanai Schrödinger equation whose solution is obtained by Ermakov mapping to a scaling function b(z) satisfying a generalized Pinney equation.