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

Dariescu, Marina–Aura

doi:10.1007/s10773-017-3595-0

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…Ciprian Dariescu wrote two papers with collaborators [134,135]. In the the first paper, using a perturbative method, Klein-Gordon equation for a charged massive field in the background of a magnetar is solved both in the interior solution and outside the star.…”

Section: Some Examples Of the Heun Equation In Physical Applicationsmentioning

confidence: 99%

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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%

“…Within the quantum analysis, the Wheeler DeWitt (WDW) equation turns into a modified Morse equation whose solutions are Mathieu and Heun functions. [135].…”

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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Quantum relativistic cosmology: Dynamical interpretation and tunneling universe

Vieira

Bezerra

Muniz

et al. 2020

Int. J. Mod. Phys. D

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In this work, the wave functions associated to the quantum relativistic universe, which is described by the Wheeler–DeWitt equation, are obtained. Taking into account different kinds of energy density, namely, matter, radiation, vacuum, dark energy and quintessence, we discuss some aspects of the quantum dynamics. In all these cases, the wave functions of the quantum relativistic universe are given in terms of the triconfluent Heun functions. We investigate the expansion of the universe using these solutions and found that the asymptotic behavior for the scale factor is [Formula: see text] for whatever the form of energy density is. On the other hand, we analyze the behavior at early stages of the universe and found that [Formula: see text]. We also calculate and analyze the transmission coefficient through the effective potential barrier.

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

Cited by 2 publications

References 16 publications

Heun Functions and Some of Their Applications in Physics

Heun Functions and Some of Their Applications in Physics

Quantum relativistic cosmology: Dynamical interpretation and tunneling universe

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