The perturbation theory model of a spherical oscillator in electric field and the vibrational stark effect in polyatomic molecular species

Petreska, Irina; Ivanovski, G.; Pejov, Ljupčo

doi:10.1016/j.saa.2006.05.010

Cited by 5 publications

(13 citation statements)

References 24 publications

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“…Note that in absence of the magnetic field (B 0 = 0), the first order correction to the ground state |0 0 0 is E (1) 0 0 0 = δ 1 2Mω 2 0 ω 0 , which is obtained in [16].…”

Section: First Order Corrections To the Energy Spectrummentioning

confidence: 94%

“…A similar problem of a spherical oscillator placed in an external homogenous electrostatic field was studied by Petreska et al [16]. In this work we consider a vector potential which in cylindrical coordinates has the following form…”

Section: The Eigenvalue Problemmentioning

confidence: 96%

“…Even though the potential energy functions for most of the polyatomic molecules are well known, and very accurate computational methods have been derived, there's still a need to search for analytically solvable forms of the Schrödinger equation, that will provide a satisfactory general model for polyatomic molecular vibrations. In previous papers by our group [16][17][18] we have investigated three-dimensional, as well as two-dimensional harmonic and anharmonic oscillator models in the presence of an external electric field. The field effects were treated using the stationary perturbation theory methodology, and it was shown that energy level splitting occurs in the presence of an electric field which could be suitably modeled by various forms of potential energy operators, perturbatively added to the non-perturbed molecular Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

“…In relation (21) = * = 2 ρ + | | + is the principal quantum number of the oscillator having the values = 0 1 2 . The energy levels of a three-dimensional isotropic harmonic oscillator in an external electric field along the z-axis are ( + 1)( + 2) 2 -fold degenerate [16], so from relation (19) one can conclude that the magnetic field removes the degeneracy of the oscillator. In absence of electric field (E = 0) the energy spectrum becomes [22] …”

mentioning

confidence: 99%

“…The parameters δ 1 δ 2 and δ 3 are phenomenological parameters that are expected to depend on both the inherent structural properties of the molecular system considered and the external electromagnetic field. Detailed explanation of some of the considered deformations is given in [16].…”

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confidence: 99%

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Axially symmetrical molecules in electric and magnetic fields: energy spectrum and selection rules

et al. 2013

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Abstract:In this paper we investigate the effects of external electric and magnetic fields on a three-dimensional harmonic oscillator with axial symmetry. The energy spectrum of such a system is non-degenerate due to the presence of the magnetic field. The degeneracy of the energy spectrum in the absence of a magnetic field is discussed. The influence of electric and magnetic fields, as well as the frequencies of the oscillator on the probability distribution function is analyzed. Optical transition probabilities are examined by deriving the selection rules in dipole approximation for the quantum numbers ρ , and . Employing stationary perturbation theory, the effects of deformations of the potential energy function on the oscillatory states are analyzed. Such models have been used in literature in analysis of spectra of axially symmetrical molecules and cylindrical quantum dots.

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“…Note that in absence of the magnetic field (B 0 = 0), the first order correction to the ground state |0 0 0 is E (1) 0 0 0 = δ 1 2Mω 2 0 ω 0 , which is obtained in [16].…”

Section: First Order Corrections To the Energy Spectrummentioning

confidence: 94%

Section: The Eigenvalue Problemmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Axially symmetrical molecules in electric and magnetic fields: energy spectrum and selection rules

et al. 2013

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Harmonic and anharmonic quantum-mechanical oscillators in noninteger dimensions

2014

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Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

Petreska

Sandev

Ivanovski

et al. 2010

Commun. Theor. Phys.

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A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonic model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a real polyatomic molecular species.

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The perturbation theory model of a spherical oscillator in electric field and the vibrational stark effect in polyatomic molecular species

Cited by 5 publications

References 24 publications

Axially symmetrical molecules in electric and magnetic fields: energy spectrum and selection rules

Axially symmetrical molecules in electric and magnetic fields: energy spectrum and selection rules

Harmonic and anharmonic quantum-mechanical oscillators in noninteger dimensions

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

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