WKB approximation for a deformed Schrodinger-like equation and its applications to quasinormal modes of black holes and quantum cosmology

Lu, Fenghua; Lv, Bochen; Wang, Peng; Yang, Haitang

doi:10.1016/j.nuclphysb.2018.06.002

Cited by 9 publications

(5 citation statements)

References 53 publications

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“…This is because at turning points, the WKB solutions break down as momentum 𝑝(𝑥) becomes 0. In order to establish the connection between the WKB solutions in the allowed region as well as in the forbidden region on either side of the breaking down point (turning point), i.e., 𝑝(𝑥) = 0, an accurate solution is needed, where the potential can be approximated as a linear potential with the slope equals the tangent of the breaking down point (See (7)), hence linking WKB solutions at a turning point [4]. However, such linear approximation only holds valid for a reasonably smooth potential.…”

Section: Approximate Solution By Wkb Methodmentioning

confidence: 99%

“…Therefore, the solutions are limited to a list of very few known potential functions, such as inverse power-law potentials, infinite and finite square wells, and parabolic potentials, and due to this fact, all physical systems are modelled with potentials from this list [1]. To overcome this limitation, many techniques have been developed to derive approximate solutions of the Schrodinger equation, and the Wentzel-Kramers-Brillouin (WKB) method is one of the most commonly used practices [2], [3], [4]. It is a power tool and it has many applications, for example, solving waves in an inhomogeneous plasma as shown in the textbook Plasma Waves (D.G.…”

Section: Introductionmentioning

confidence: 99%

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Application of WKB Method in Approximating Wave Functions in Square Potential Wells

Guo

2022

J. Phys.: Conf. Ser.

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This paper introduces a widely used approximation method, the Wentzel-Kramers-Brillouin (WKB) method, for solving the Schrodinger equation, sets up a theoretical framework to derive the general solutions of the method, and carries out the application of the approximation method in specific cases to verify the validity and practicality of the method. Throughout the study, numerical methods, such as the Simpsons method, and programming tools, such as Python, are used to process sophisticated calculations. The final approximated solutions for the Schrodinger equation are able to demonstrate the state of a particle in an isolated quantum system. All the presented studies are based upon the knowledge and skillsets of a high school student.

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Section: Approximate Solution By Wkb Methodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of WKB Method in Approximating Wave Functions in Square Potential Wells

Guo

2022

J. Phys.: Conf. Ser.

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“…In order to discuss the effect of the nonlocality on the distribution of the energy levels for the trapped nonlocal field we consider the same parabolic potential (47) as in the previous subsection, but modify the kinetic part of the effective Hamiltonian. We use dimensionless units defined in the footnote 2 and denote…”

Section: Phase Trajectoriesmentioning

confidence: 99%

“…In these paper we apply this method for study quasiclassical solutions of the linear nonlocal scalar field equations in the presence of an external potential. A similar approach for other higher and infinite order equations can be found in [47].…”

Section: Introductionmentioning

confidence: 98%

Nonlocal scalar field in an external potential: WKB approximation

Frolov

2020

Preprint

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We consider a nonlocal theory of a scalar massive field in a flat spacetime background in the presence of an external potential and construct WKB solutions for this theory. We use a model in which the kinetic part of the scalar field action is modified by changing to f ( ) operator. We discuss conditions when the corresponding form factor f is chosen so that the theory does not contain new unphysical degrees of freedom. We applied the obtained WKB solutions for study energy levels of the field trapped by a one-dimensional potential and the probability of the barrier penetration. This allows us to illustrate how the effects of the nonlocality change the known results obtained for the local field theory.

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“…Specifically, Various approaches have been employed to examine the resolutions of the Schrödinger formula with different types of potentials. [10][11][12][13][14][15][16] The objective of this study is to incorporate the NU into the existing framework [17],…”

Section: Introductionmentioning

confidence: 99%

Energy spectrum of selected diatomic molecules (H2, CO, I2, NO) by the resolution of Schrodinger equation for combined potentials via NUFA method

Reggab

2024

J Mol Model

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The equation proposed by Schrödinger is widely recognized as the foundational formula in quantum science, comparable to the law of gravity in the study of classical physics.Describing phenomena in various fields, such as quantum optics and atomic physics, exhibits significant diversity. For specific diatomic molecule potentials, analytical responses to the Schrodinger formula can be found. These responses cover all possible values of angular momentum. The NU functional analysis and the Greene-Aldrich hypothesis are employed in our study for the purpose of obtaining an approximate solution for the Schrödinger issue including a screened modified Kratzer potential combined with an inverse quadratic Yukawa potential, a systematic approach needs to be employed. In this study, we calculate the energy eigenvalues associated with bound states in various quantum states, the present study focuses on a distinct group of diatoms molecules. The analytical data that were acquired are utilized in the analysis of various diatomic compounds H2, CO, I2, and NO. A comparative analysis compares the results of this study to those found in other studies that used different methods to figure out how accurate the current method is.

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WKB approximation for a deformed Schrodinger-like equation and its applications to quasinormal modes of black holes and quantum cosmology

Cited by 9 publications

References 53 publications

Application of WKB Method in Approximating Wave Functions in Square Potential Wells

Application of WKB Method in Approximating Wave Functions in Square Potential Wells

Nonlocal scalar field in an external potential: WKB approximation

Energy spectrum of selected diatomic molecules (H2, CO, I2, NO) by the resolution of Schrodinger equation for combined potentials via NUFA method

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