Classical applications of the Klein–Gordon equation

Gravel, Pierre; Gauthier, Claude

doi:10.1119/1.3559500

Cited by 31 publications

(19 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The hyperbolic Klein–Gordon equation is useful in different physical theories, for example, in solid state physics, quantum field theory, classical mechanics, and nonlinear optics [ 19 , 20 ]:

…”

Section: Introductionmentioning

confidence: 99%

Time-Fractional Diffusion with Mass Absorption in a Half-Line Domain due to Boundary Value of Concentration Varying Harmonically in Time

Povstenko

Kyrylych

2018

Entropy

View full text Add to dashboard Cite

The time-fractional diffusion equation with mass absorption is studied in a half-line domain under the Dirichlet boundary condition varying harmonically in time. The Caputo derivative is employed. The solution is obtained using the Laplace transform with respect to time and the sin-Fourier transform with respect to the spatial coordinate. The results of numerical calculations are illustrated graphically.

show abstract

…”

Section: Introductionmentioning

confidence: 99%

Time-Fractional Diffusion with Mass Absorption in a Half-Line Domain due to Boundary Value of Concentration Varying Harmonically in Time

Povstenko

Kyrylych

2018

Entropy

View full text Add to dashboard Cite

show abstract

“…The equation has a large range of applications in contemporary physics, including particle physics, astrophysics, cosmology, classical mechanics, etc. (see [1][2][3][4] and references therein). For the stationary problems, when the Hamiltonian does not depend on time, particular solutions can be obtained by applying the separation of variables that reduces the problem to the solution of the stationary Klein-Gordon equation.…”

Section: Introductionmentioning

confidence: 99%

Four five‐parametric and five four‐parametric independent confluent Heun potentials for the stationary Klein‐Gordon equation

Tarloyan

Ishkhanyan

2016

Annalen der Physik

View full text Add to dashboard Cite

We present in total fifteen potentials for which the stationary Klein-Gordon equation is solvable in terms of the confluent Heun functions. Because of the symmetry of the confluent Heun equation with respect to the transposition of its regular singularities, only nine of the potentials are independent. Four of these independent potentials are five-parametric. One of them possesses a four-parametric ordinary hypergeometric sub-potential, another one possesses a four-parametric confluent hypergeometric sub-potential, and one potential possesses four-parametric sub-potentials of both hypergeometric types. The fourth fiveparametric potential has a three-parametric confluent hypergeometric sub-potential, which is, however, only conditionally integrable. The remaining five independent Heun potentials are four-parametric and have solutions only in terms of irreducible confluent Heun functions.

show abstract

“…Gravel and Gauthier arrived at same result in [3], and Mouchet in [4], when discussing a classical use of the Klein-Gordon equation, which has the same mathematical form as (2) with κ(x) = κ. From (9) it can be seen that the wavenumber is imaginary whenever the natural frequency of a lone oscillator ω κ is greater than the driving frequency.…”

Section: Introductionmentioning

confidence: 80%

A mechanical wave system to show waveforms similar to quantum mechanical wavefunctions in a potential

Faletič

2015

Eur. J. Phys.

View full text Add to dashboard Cite

Interviews with students suggest that even though they understand the formalism and the formal nature of quantum theory, they still often desire a mental picture of what the equations describe and some tangible experience with the wavefunctions. Here we discuss a mechanical wave system capable of reproducing correctly a mechanical equivalent of a quantum system in a potential, and the resulting waveforms in principle of any form. We have successfully reproduced the finite potential well, the potential barrier and the parabolic potential. We believe that these mechanical waveforms can provide a valuable experience base for introductory students to start from. We aim at showing that mechanical systems that are described with the same mathematics as quantum mechanical, indeed behave in the same way. We believe that even if treated as a purely wave phenomenon, the system provides much insight into wave mechanics. This can be especially useful for physics teacher and others who often need to resort to concepts and experience rather than mathematics when explaining physical phenomena.

show abstract

Classical applications of the Klein–Gordon equation

Cited by 31 publications

References 4 publications

Time-Fractional Diffusion with Mass Absorption in a Half-Line Domain due to Boundary Value of Concentration Varying Harmonically in Time

Time-Fractional Diffusion with Mass Absorption in a Half-Line Domain due to Boundary Value of Concentration Varying Harmonically in Time

Four five‐parametric and five four‐parametric independent confluent Heun potentials for the stationary Klein‐Gordon equation

A mechanical wave system to show waveforms similar to quantum mechanical wavefunctions in a potential

Contact Info

Product

Resources

About