Abstract
It is known that the exact solutions of non-relativistic and relativistic equations in the spherically central fields have become an important subject in quantum mechanics. As illustrated above, the main contributions have been made to the Schrödinger and Dirac equations. During the past several decades, however, the Klein-Gordon equation with the Coulomb potential has been studied in three dimensions such as the operator analysis, in an intense laser field, in two dimensions and in one dimension. On the other hand, the Klein-Gordon equation with a Coulomb potential in (D+1) dimensions has been discussed by the different approaches like the large-N expansion approximate method. The purpose of this Chapter is to present the Klein-Gordon equation in arbitrary dimensions and solve the hydrogen-like atom problem.
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References
Nieto, M.M.: Hydrogen atom and relativistic pi-mesic atom in N-space dimensions. Am. J. Phys. 47, 1067 (1979)
Chatterjee, A.: Large-N solution of the Klein-Gordon equation. J. Math. Phys. 27, 2331 (1986)
de Lange, O.L.: An operator analysis for the Schrödinger, Klein-Gordon, and Dirac equations with a Coulomb potential. J. Math. Phys. 30, 858 (1989)
Faisal, F.H.M., Radozycki, T.: Three-dimensional relativistic model of a bound particle in an intense laser field. II. Phys. Rev. A 48, 554–557 (1993)
Dong, S., Dong, S.H.: Schrödinger equation with a Coulomb field in 2+1 dimensions. Phys. Scr. 66, 342–344 (2002)
Spector, H.N., Lee, J.: Relativistic one-dimensional hydrogen atom. Am. J. Phys. 53, 248 (1985)
Moss, R.E.: The hydrogen atom in one dimension. Am. J. Phys. 55, 397 (1987)
Galić, H.: Fun and frustration with hydrogen in a 1+1 dimension. Am. J. Phys. 56, 312 (1988)
Levy, A.A.: Systematic comparison of the quantization rules of hydrogenoid atoms in the Old Quantum, Schrödinger, Klein-Gordon, and Dirac theories, by means of a common set of three parameters. Am. J. Phys. 53, 454 (1985)
Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals, Series, and Products, 5th edn. Pergamon, New York (1994)
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Dong, SH. (2011). Klein-Gordon Equation in Higher Dimensions. In: Wave Equations in Higher Dimensions. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1917-0_5
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DOI: https://doi.org/10.1007/978-94-007-1917-0_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-1916-3
Online ISBN: 978-94-007-1917-0
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