Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

A. Kamenshchik; M. Luzzi; G. Venturi

DOI:10.1007/s11182-010-9375-4
Corpus ID: 9410225

Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

@inproceedings{Kamenshchik2005RemarksOT,
  title={Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation},
  author={Alexander Yu. Kamenshchik and Mattia Luzzi and Giovanni Venturi},
  year={2005}
}

A. KamenshchikM. LuzziG. Venturi
Published 8 June 2005
Mathematics, Physics

The connection between the method of comparison equations (generalized WKB method) and the Ermakov-Pinney equation is established. A perturbative scheme of solution of the generalized Ermakov-Pinney equation is developed and is applied to the construction of perturbative series for second-order diﬀerential equations with and without turning points.

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14 Citations

Background Citations

Methods Citations

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Physics
2006

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2018

A cosmological extension of the Eisenhart–Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed…

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2006

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Physics
2009

We report a method of solving for canonical scalar field exact solution in a non-flat FLRW universe with barotropic fluid using non-linear Schrödinger (NLS)-type formulation in comparison to the…

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Physics, Mathematics
2020

Time-independent nonlinear Schrodinger-type (NLS) formulation of FRW cosmology with canonical scalar field is considered in the case of two barotropic fluids. We derived Friedmann formulation varia...

Solvable Time-Dependent Models in Quantum Mechanics

R. Cordero-Soto
Physics
2011

In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrödinger equations with time-dependent Hamiltonians have been solved, explicitly…

Quantum gravity, time, bounces, and matter

A. KamenshchikA. TronconiT. VardanyanG. Venturi
Physics
Physical Review D
2018

In the context of Quantum Cosmology and the Wheeler-DeWitt equation we investigate the possible effects of a non semiclassical wave-function of the universe on the evolution of the inflationary…

Energy exchange in the dissipative time-dependent harmonic oscillator: Physical interpretation of the Ermakov invariant

M. F. Guasti
Materials Science
Pramana
2022

The energy of a mechanical system as well as other invariants can be obtained using a complementary variable formulation. This approach is extended here to systems with a dissipative force. The…

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