Quantum Analysis of $$k=-1$$ k = - 1 Robertson–Walker Universe

Dariescu, Ciprian

doi:10.1007/s10701-015-9922-5

Cited by 3 publications

(1 citation statement)

References 27 publications

(44 reference statements)

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“…Dariescu, [117], the solutions are in terms of double confluent Heun functions. Same authors also published Quantum analysis of k=-1 Robert-Walker Universe, where they solved the Wheeler-DeWitt equation [118]. The solutions turned out to be Heun functions.…”

Section: Some Examples Of the Heun Equation In Physical Applicationsmentioning

confidence: 99%

Heun Functions and Some of Their Applications in Physics

Hortaçsu

2018

Advances in High Energy Physics

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Most of the theoretical physics known today is described by using a small number of differential equations. For linear systems, different forms of the hypergeometric or the confluent hypergeometric equations often suffice to describe the system studied. These equations have power series solutions with simple relations between consecutive coefficients and/ or can be represented in terms of simple integral transforms. If the problem is nonlinear, one often uses one form of the Painlevé equations. There are important examples, however, where one has to use higher order equations. Heun equation is one of these examples, which recently is often encountered in problems in general relativity and astrophysics. Its special and confluent forms take names as Mathieu, Lamé and Coulomb spheroidal equations. For these equations whenever a power series solution is written, instead of a two way recursion relation between the coefficients in the series, we find one between three or four different ones. An integral transform solution using simpler functions also is not obtainable.The use of this equation in physics and mathematical literature exploded in the later years, more than doubling the number of papers with these solutions in the last decade, compared to time period since this equation was introduced in 1889 up to 2008. We use SCI data to conclude this statement, which is not precise, but in the correct ballpark. Here this equation will be introduced and examples for its use, especially in general relativity literature will be given. * This paper is a revised and many times updated version of the conference talk by the same author, published in

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Section: Some Examples Of the Heun Equation In Physical Applicationsmentioning

confidence: 99%

Heun Functions and Some of Their Applications in Physics

Hortaçsu

2018

Advances in High Energy Physics

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Mathieu and Heun Solutions to the Wheeler–De Witt Equation for Hyperbolic Universes

Dariescu

2017

Int J Theor Phys

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Quantum cosmology on (k = −1)-Friedmann–Robertson–Walker Universe evolving from stiff matter era to the dust dominated one

Dariescu

2016

Mod. Phys. Lett. A

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This work is devoted to the spatially open Friedmann–Robertson–Walker (FRW) Universe evolving from the stiff matter era to the dust dominated one. Within the quantum analysis based on the Wheeler–DeWitt equation, we derive the wave function of the [Formula: see text]-FRW Universe with combined matter sources. On the classical level, one has to deal with the Friedmann equation which leads on a dependence of the scale function on time generally expressed from functional relations involving elliptic integrals.

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Quantum Analysis of $$k=-1$$ k = - 1 Robertson–Walker Universe

Cited by 3 publications

References 27 publications

Heun Functions and Some of Their Applications in Physics

Heun Functions and Some of Their Applications in Physics

Mathieu and Heun Solutions to the Wheeler–De Witt Equation for Hyperbolic Universes

Quantum cosmology on (k = −1)-Friedmann–Robertson–Walker Universe evolving from stiff matter era to the dust dominated one

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