Excited states of spherium

Loos, Pierre‐François; Gill, Peter M. W.

doi:10.1080/00268976.2010.508472

Cited by 44 publications

(51 citation statements)

References 66 publications

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“…One can note the similarity of the three-term recurrence relation obtained for R 1 = R 2 [10][11][12] and the term in square brackets in (17). The condition s 1 = 0 shows that the exact wave functions do not contain any term proportional to the interelectronic distance u.…”

Section: Exact Solutionsmentioning

confidence: 99%

“…In a recent series of papers [10][11][12], we have found exact solutions for several new quasi-exactly solvable models. In particular, we have shown that one can solve the Schrödinger equation for two electrons confined to a ring [12] or to the surface of a sphere [10,11] for particular values of the ring or sphere radius.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, we have shown that one can solve the Schrödinger equation for two electrons confined to a ring [12] or to the surface of a sphere [10,11] for particular values of the ring or sphere radius. In particular, we showed that some of the solutions exhibit the Berry phase phenomenon, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Exact wave functions for concentric two-electron systems

Loos¹,

Gill²

2014

Physics Letters A

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Section: Exact Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact wave functions for concentric two-electron systems

Loos¹,

Gill²

2014

Physics Letters A

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“…This is in agreement with the result of Pechukas who showed that, when two nodal surfaces cross, they are perpendicular at the crossing point. 38 We have recently shown that, for certain states such as the 3 P o (sp), 3 P e (p 2 ), 3 D e (sd) and 3 D o (pd) states, exact solutions of the Schrödinger equation can be found in closed form for specific values of the radius R. 39,40 Even though the exact closed-form expression of the Schrödinger equation is only known for particular values of the radius, their exact nodes are analytically known for all radii (see Table I). …”

Section: Proof Of the Exactness Of The Nodesmentioning

confidence: 99%

“…These are the 1 S e (s 2 ), 1 P o (sp), 1 D o (pd) and 1 F e (pf ) states. 40 These singlet states are connected to their triplet partner by exact interdimensional degeneracies. [40][41][42] Two states in different dimensions are said to be interdimensionally degenerated when their energies are the same.…”

Section: Interdimensional Degeneraciesmentioning

confidence: 99%

Nodal surfaces and interdimensional degeneracies

Loos

Bressanini

2015

The Journal of Chemical Physics

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The aim of this paper is to shed light on the topology and properties of the nodes (i.e. the zeros of the wave function) in electronic systems. Using the "electrons on a sphere" model, we study the nodes of two-, threeand four-electron systems in various ferromagnetic configurations (sp, p 2 , sd, pd, p 3 , sp 2 and sp 3 ). In some particular cases (sp, p 2 , sd, pd and p 3 ), we rigorously prove that the non-interacting wave function has the same nodes as the exact (yet unknown) wave function. The number of atomic and molecular systems for which the exact nodes are known analytically is very limited and we show here that this peculiar feature can be attributed to interdimensional degeneracies. Although we have not been able to prove it rigorously, we conjecture that the nodes of the non-interacting wave function for the sp 3 configuration are exact.

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Spectra of electron pair under harmonic and Debye potential

Munjal

Prasad

2017

Contributions to Plasma Physics

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Two electron systems confined by harmonic potential is known as harmonium. Such a system has been studied for many reasons in the literature. In this work we study harmonium under Debye potential. We use higher order finite difference method for the solution of Schrodinger equation. Complete energy spectrum of harmonium and harmonium under Debye potential is studied. Debye screening length shows considerable effect on the energy levels and the radial matrix elements. The results are analysed in the light of existing results and the comparison with available results shows remarkable agreement. KEYWORDSconfined harmonium, Debye potential, radial matrix element INTRODUCTIONThe study of confined atoms was initiated by Michels et al. [1] in 1937 in order to study the effect of high pressure on atomic hydrogen. Since then much of the work has been devoted to study confined atoms. Confined quantum systems have attracted many studies owing to their importance in the physics of quantum heterostructures, where, off late, many new structures are being proposed. [2][3][4][5][6][7] A few structures in various environments are studied using approximate potentials such as power series potentials and screened coulomb Debye potential. [8] The confinement and atoms under confinement have been studied in various interdisciplinary studies. [9][10][11][12][13][14][15][16][17] The study of such systems has gained importance because of technological importance of atoms, molecules, and ions in cavity and excitons in semiconductor heterostructures. [18,19] In addition, it is also a very well-known fact that the chemical reactivity of confined systems shows drastic change with change of confinement, hence it has led to many applications. Even atoms with high atomic numbers have been studied in different confinements. Jiao et al. [20] studied spectral and structural data of He atom under screened coulomb potential. Ghoshal and Ho [21] studied the ground state of two-electron system in generalized screened potential. Jiang et al. [22] studied this system under Lorentzian astrophysical plasma. Two interacting electrons with or without harmonic potential form a system that attracts a lot of interest. Two interacting electron system is a model system which is used to explore the physical aspects of many phenomena involving several electron systems. Two electrons confined in an infinite spherical well has been well studied theoretically. [23][24][25][26][27][28] Study of harmonium atom can be helpful in density functional theory and to study the optical properties of two-electron quantum dot. Even harmonium atom with more than two electrons [29][30][31][32] is also well studied in the literature due to its usefulness in solid state physics and quantum chemistry. Here, we study in detail the properties of harmonium in Debye environment. We solve this problem using eighth order finite difference method to describe the relative motion of the system. The effectiveness of our method is shown by comparing our results with those of available data for ...

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Excited states of spherium

Cited by 44 publications

References 66 publications

Exact wave functions for concentric two-electron systems

Exact wave functions for concentric two-electron systems

Nodal surfaces and interdimensional degeneracies

Spectra of electron pair under harmonic and Debye potential

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