Addendum: “On the Dirac equation for the hydrogen atom’’ [Am. J. Phys. <b>47</b>, 1098 (1979)]

Waldenstrøm, S.

doi:10.1119/1.12032

Cited by 14 publications

(16 citation statements)

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“…The eigenvalues as well as their fine structure energy are also studied. Our solutions coincide with those in 3+1 dimensional [21] and 2+1 dimensional [22] space-time.…”

Section: Discussionsupporting

confidence: 77%

“…The eigenvalues as well as their fine structure energy are also studied. Our solutions coincide with those in 3+1 dimensional [21] and 2+1 dimensional [22] space-time. ACKNOWLEDGMENTS S.-H. Dong would like to thank Professor A. Frank for the hospitality in UNAM.…”

Section: Discussionsupporting

confidence: 77%

“…The nonrelativistic D-dimensional Coulombic and the harmonic oscillator problems have been studied in some detail by many authors [9,10,11,12,13,14,15]. The solutions of the Dirac equation, however, have been studied in the usual three- [17,18,19,20,21], two- [22] and one-dimensional [23] space. Motivated by the recent interest of higher-dimensional field theory , we generalize the Dirac equation to D+1 space-time.…”

Section: Introductionmentioning

confidence: 99%

“…Eq. ( 41) can be solved by the power series expansion method for for (3+1)-dimensions [21] and (2+1)-dimensions [22]. The results in D + 1 dimensions are as follows…”

mentioning

confidence: 99%

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Exact Solutions to the Dirac Equation for a Coulomb Potential in D + 1 Dimensions

Zhong

Dong

2002

Int. J. Mod. Phys. E

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The Dirac equation is generalized to D + 1 space-time. The conserved angular momentum operators and their quantum numbers are discussed.The eigenfunctions of the total angular momenta are calculated for both odd D and even D cases. The radial equations for a spherically symmetric system are derived. The exact solutions for the system with a Coulomb potential are obtained analytically. The energy levels and the corresponding fine structure are also presented.

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“…The eigenvalues as well as their fine structure energy are also studied. Our solutions coincide with those in 3+1 dimensional [21] and 2+1 dimensional [22] space-time.…”

Section: Discussionsupporting

confidence: 77%

Section: Discussionsupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

“…Eq. ( 41) can be solved by the power series expansion method for for (3+1)-dimensions [21] and (2+1)-dimensions [22]. The results in D + 1 dimensions are as follows…”

mentioning

confidence: 99%

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Exact Solutions to the Dirac Equation for a Coulomb Potential in D + 1 Dimensions

Zhong

Dong

2002

Int. J. Mod. Phys. E

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“…In particular, the relativistic Dirac equation, which plays an important role in the understanding of many quantum mechanical problems, has been solved with various physical potentials. For instance, the solutions of the Dirac equation with the Coulomb potential have been obtained in 1D [39,40], 2D [41], and 3D [42][43][44]. The Dirac-Hulthén problem with PDM in D-dimensions has also been discussed [45] and the spin-symmetry case of the Dirac equation has also been discussed both in 3D [46] and in D-dimensions [47].…”

Section: Agboolamentioning

confidence: 99%

Bound‐states of diatomic molecules in the Dirac equation with the q‐deformed Morse potential

Agboola

2011

Int J of Quantum Chemistry

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ABSTRACT:We present the solutions of the ro-vibrational motion of a diatomic molecule with a spatially dependent mass by solving the Dirac equation with position-dependent mass for repulsive vector V(r) and attractive scalar S(r) q-deformed Morse potential for any κ value, within the framework of Pekeris approximation of the spin-orbit coupling term. The relativistic energy spectra are obtained using the Nikiforov-Uvarov method and the two-component spinor wavefunctions are obtained in terms of the Laguerre polynomials. It is found that there exist only negative energy states for bound states, and the energy values for a fixed value of n r increase with decrease in κ.

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A discussion on the relativistic corrections of the electronic structures of multi‐electron atoms

Nanni

2023

Int J of Quantum Chemistry

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The theory of special relativity is a topic not addressed in theoretical chemistry courses. Einstein's theory of relativity is mainly applied to high‐energy phenomena governed by physical laws not used to describe the chemical bond. Nevertheless, the electrons of heavy elements orbit around the nucleus with relativistic velocities. Here it is, then, the laws that appeared so unusual for chemistry became fundamental tools for investigating the properties of these atoms. Studying the electronic structure of heavy elements is the best place for chemists to learn to tame the pitfalls of a little‐known subject, such as Einstein's theory, and become familiar with its elegant formalism. In this paper, the main relativistic approaches to quantum chemistry are revisited. The problem of the finite nuclear size, the approximation methods used to solve the relativistic equations for k‐shell electrons, and the problem of the negative energy continuum are investigated. Some ansatzes to solve divergence's problem of relativistic corrections near the nucleus are proposed. Finally, a possible connection between the self‐consistent field method and bondonic chemistry is also investigated.

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Addendum: “On the Dirac equation for the hydrogen atom’’ [Am. J. Phys. 47, 1098 (1979)]

Cited by 14 publications

References 0 publications

Exact Solutions to the Dirac Equation for a Coulomb Potential in D + 1 Dimensions

Exact Solutions to the Dirac Equation for a Coulomb Potential in D + 1 Dimensions

Bound‐states of diatomic molecules in the Dirac equation with the q‐deformed Morse potential

A discussion on the relativistic corrections of the electronic structures of multi‐electron atoms

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