Orthogonality criteria for singular states and the nonexistence of stationary states with even parity for the one-dimensional hydrogen atom

Dai, Xianxi; Dai, Jufeng; JiQiong, Dai

doi:10.1103/physreva.55.2617

Cited by 42 publications

(39 citation statements)

References 12 publications

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“…In part, this can be attributed to the ongoing controversy concerning the mathematical structure of the eigenfunctions. [57][58][59][60][61][62][63] Although debates about the parities and boundedness of the eigenfunctions continue, we will assume in the present study that nuclei are impenetrable. 57,61,64 In Sec.…”

Section: D Chemistrymentioning

confidence: 99%

Chemistry in one dimension

Loos

Ball

Gill

2015

Phys. Chem. Chem. Phys.

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We report benchmark results for one-dimensional (1D) atomic and molecular systems interacting via the Coulomb operator |x| −1 . Using various wavefunction-type approaches, such as Hartree-Fock theory, second-and third-order Møller-Plesset perturbation theory and explicitly correlated calculations, we study the ground state of atoms with up to ten electrons as well as small diatomic and triatomic molecules containing up to two electrons. A detailed analysis of the 1D helium-like ions is given and the expression of the high-density correlation energy is reported. We report the total energies, ionization energies, electron affinities and other interesting properties of the many-electron 1D atoms and, based on these results, we construct the 1D analog of Mendeleev's periodic table. We find that the 1D periodic table contains only two groups: the alkali metals and the noble gases. We also calculate the dissociation curves of various 1D diatomics and study the chemical bond in H + 2 , HeH 2+ , He 3+ 2 , H 2 , HeH + and He 2+ 2 . We find that, unlike their 3D counterparts, 1D molecules are primarily bound by one-electron bonds. Finally, we study the chemistry of H + 3 and we discuss the stability of the 1D polymer resulting from an infinite chain of hydrogen atoms.

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Section: D Chemistrymentioning

confidence: 99%

Chemistry in one dimension

Loos

Ball

Gill

2015

Phys. Chem. Chem. Phys.

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“…26 In this last work, it was concluded that the Klein-Gordon equation, with the interacting potential considered as a time component of a vector, provides unacceptable solutions while the Dirac equation has no bounded solutions at all. On the other hand, in a more recent work, 23 the authors use connection conditions for the eigenfunctions and their first derivatives across the singularity of the potential and conclude that only the odd-parity solutions of the Schrödinger equation survive. The problem was also sketched for a Lorentz scalar potential in the Dirac equation in Refs.…”

Section: Introductionmentioning

confidence: 99%

On Duffin–Kemmer–Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound-states for the one-dimensional inversely linear background

Castro

2010

Journal of Mathematical Physics

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The problem of spin-0 and spin-1 bosons in the background of a general mixing of minimal and nonminimal vector inversely linear potentials is explored in a unified way in the context of the Duffin-Kemmer-Petiau theory. It is shown that spin-0 and spin-1 bosons behave effectively in the same way. An orthogonality criterion is set up and it is used to determine uniquely the set of solutions as well as to show that even-parity solutions do not exist.

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“…Spector and Lee [17] presented a relativistic treatment that removed the problem of infinite binding energy of the ground state. Several other works [18,19,20,21,22,5,23,24] (see also references therein) have discussed this (apparent) simple problem.…”

Section: Lower Dimensional Hydrogen Atommentioning

confidence: 99%