The oscillator representation and the stability of three-body Coulomb systems

Dineykhan, M.; Efimov, G. V.

doi:10.1007/bf01074542

Cited by 9 publications

(16 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore the validity of Hund's rules in an anharmonic case has not been addressed, so far. A similar effect has been seen earlier for the quantum dot model, where the spin symmetry of the ground state depends on the applied magnetic field 20 . Measurements of the electric current through a single quantum dot depending on the applied gate voltage show a specific shell structure of the ground state energies for few electrons confined in the dot 21,22 .…”

Section: Introductionsupporting

confidence: 82%

Exact treatment of planar two-electron quantum dots: Effects of anharmonicity on the complexity

et al. 2013

View full text Add to dashboard Cite

Static properties of an anharmonic potential model for planar two-electron quantum dots are investigated using a method which allows for the exact representation of the matrix elements, including the full Coulombic electron -electron interaction. The anharmonic confining potential in combination with the interparticle Coulomb interaction affects the spectral properties of the system considerably as it implies total loss of separability of the system. Properties of the classical phase space, spectral measures of the chaoticity, as well as localization properties of the eigenstates corroborate this.

show abstract

Section: Introductionsupporting

confidence: 82%

Exact treatment of planar two-electron quantum dots: Effects of anharmonicity on the complexity

et al. 2013

View full text Add to dashboard Cite

show abstract

“…This problem has been addressed by many authors, in textbooks [89, p. 286], in review papers [53], or in articles, see for instance [10,120,121,122,123,124,125,126,127], and references therein.…”

Section: A General Approach To Three Unit-charge Systemsmentioning

confidence: 99%

“…In Ref. [124], an astute changes of variables makes it possible to use harmonic-oscillator type of wave functions, but while the binding energy of symmetric states with m 2 = m 3 are accurately computed, the stability domain of states with m 2 = m 3 extends too far, with, e.g., (M + , M − , m ± ) leaving stability for M/m > 2.45, while Mitroy [5] found it unstable. Clearly, more cross-checks of the published results are needed.…”

Section: A General Approach To Three Unit-charge Systemsmentioning

confidence: 99%

Stability of few-charge systems in quantum mechanics

2005

View full text Add to dashboard Cite

We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the studies that have been made of specific mass configurations and also the properties of the domain of stability in the space of masses or inverse masses. These rigorous results are supplemented by numerical investigations using accurate variational methods. A section is devoted to systems of three arbitrary charges and another to molecules in a world with two space-dimensions.

show abstract

“…In this paper, the oscillator representation method ( [5,6]) will be applied to calculate the energy spectrum axial symmetrical potentials. The most remarkable difference between Quantum Field Theory and Quantum Mechanics is that quantized fields in QFT are sets of oscillators and any interactions of fields do not change the oscillator nature of these quantized fields.…”

Section: Introductionmentioning

confidence: 99%

Axially symmetric potentials in the oscillator representation

Dineykhan

1997

Z Phys D - Atoms, Molecules and Clusters

Self Cite

View full text Add to dashboard Cite

The Wick-ordering method called the Oscillator Representation in the nonrelativistic Schrödinger equation is proposed to calculate the energy spectrum for axially symmetric potentials allowing the existence of a bound state. In particular, the method is applied to calculate the energy spectrum of (2s) states of a hydrogen atom in a uniform magnetic field of an arbitrary strength. In the perturbation (external field) approximation, the energy spectrum of the so-called quadratic and spherical quadratic Zeeman problem and the problem of a hydrogen atom in a generalized van der Waals potential is calculated analytically. The results of the zeroth approximation of oscillator representation are in good agreement with the exact values.

show abstract

The oscillator representation and the stability of three-body Coulomb systems

Cited by 9 publications

References 22 publications

Exact treatment of planar two-electron quantum dots: Effects of anharmonicity on the complexity

Exact treatment of planar two-electron quantum dots: Effects of anharmonicity on the complexity

Stability of few-charge systems in quantum mechanics

Axially symmetric potentials in the oscillator representation

Contact Info

Product

Resources

About