A study of the confined 2D isotropic harmonic oscillator in terms of the annihilation and creation operators and the infinitesimal operators of the SU(2) group

Stevanović, Lj.; Sen, K. D.

doi:10.1088/1751-8113/41/26/265203

Cited by 11 publications

(6 citation statements)

References 23 publications

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“…The problem of a molecular system in a cavity of a finite size has been a popular topic since the 1930s in the context of solid state physics [1][2][3][4], systems under high pressure [5], and astrophysics [6] and also attracts considerable attention as a simple model of a molecule trapped into a structure defect of a crystal solid or a nanostructure (see [7][8][9][10][11][12][13] and the references therein). Mathematically, the encapsulation of a system into an impenetrable cavity corresponds to the Dirichlet boundary condition, i.e.…”

Section: Introductionmentioning

confidence: 99%

States of a hydrogen atom in an impenetrable cubic cavity

Kretov¹,

Scherbinin²,

Пупышев³

2009

Phys. Scr.

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Changes in the relative positions of energy levels of a hydrogen atom placed into an impenetrable cubic cavity under both variations of the cavity size and nuclear displacements off the center alongside the fourfold symmetry axes are studied. Numerical estimates for the energies of the states corresponding to 1s, 2s, 2p, 3d states in the free atom, are performed using the collocation method for cavities with edge lengths within 1 to 6 au. Qualitative methods that may be used to analyze the changes in the atomic states in a cubic cavity under variations of its form or nuclear displacements are discussed.

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Section: Introductionmentioning

confidence: 99%

States of a hydrogen atom in an impenetrable cubic cavity

Kretov¹,

Scherbinin²,

Пупышев³

2009

Phys. Scr.

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“…A recipe was also provided for 3DCHO within the super-symmetric quantum mechanics [45] in association with variational principle, as well as a generalized pseudospectral (GPS) method [46,47]. Eigenspectra of 2DCHO [48] and 3DCHO [49] were investigated analytically in terms of annihilation and creation operators. A combination of semi-classical WKB method and a proper quantization rule [50] has also been suggested for the spherically confined harmonic oscillator.…”

Section: Introductionmentioning

confidence: 99%

Information analysis in free and confined harmonic oscillator

Mukherjee¹,

Roy²

2021

Preprint

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In this chapter we shall discuss the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator (CHO). Confined quantum systems have provided appreciable interest in areas of physics, chemistry, biology, etc., since its inception. A particle under extreme pressure environment unfolds many fascinating, notable physical and chemical changes. The desired effect is achieved by reducing the spatial boundary from infinity to a finite region. Similarly, in the last decade, information measures were investigated extensively in diverse quantum problems, in both free and constrained situations. The most prominent amongst these are: Fisher information (I), Shannon entropy (S), Rényi entropy (R), Tsallis entropy (T ), Onicescu energy (E) and several complexities. Arguably, these are the most effective measures of uncertainty, as they do not make any reference to some specific points of a respective Hilbert space. These have been invoked to explain several physico-chemical properties of a system under investigation. Kullback-Leibler divergence or relative entropy describes how a given probability distribution shifts from a reference distribution function. This characterizes a measure of discrimination between two states. In other words, it extracts the change of information in going from one state to another.The one-dimensional confined harmonic oscillator (1DCHO), defined by v), can be classified into two forms, (a) symmetrically confined harmonic oscillator (SCHO) (when d m = 0), (b) asymmetrically confined harmonic oscillator (ACHO) (corresponding to d m = 0). Further, in latter case, confinement can be accomplished two different ways: (i) by changing the box boundary, keeping box length and d m fixed at zero; (ii) another route is to adjust d m by keeping box length and boundary fixed. SCHO can be treated as an intermediate between a particle-ina-box (PIB) and a 1DQHO. Though the Schrödinger equation for SCHO can be solved exactly, for ACHO it cannot be. We have employed two different methods for the latter, viz., (i) an imaginary time propagation (ITP), leading to minimization of an expectation value (ii) a variation-induced exact diagonalization procedure that utilizes SCHO eigenfunctions as basis. It is found that, at very low x c region, I, S, R, T, E remain invariant with change confinement length, x c . At moderate x c region S x , R x , T x progress and I x , E x decrease with rise in x c . Additionally, special attention has been paid to study relative information in SCHO and ACHO.Analogously, a 3DCHO (radically confined within an impenetrableFree and confined harmonic oscillator • • • spherical well) can act as a bridge between particle in a spherical box (PISB) and isotropic 3DQHO. The time-independent Schrödinger equation for D-dimensional harmonic oscillator in both free and confined condition can be solved exactly, within a Dirichlet boundary condition. Here a detailed exploration of information measures has been carried out in r and p spaces, for a 3DCHO. Some ex...

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“…In the one-dimensional (1D) model, the HO is located in the center of the potential enclosure, while in the 3D HO and the one-electron atoms, a spherical wall is impossed. The HO, a general model for systems that involves vibrations, and the compressed hydrogen, a benchmark of confined atomic systems, are extensively used for testing new methodologies [20,[39][40][41][42][43][44][45][46][47][48][49][50][51][52]. As an example we cite the harmonic QDs where electrons are confined by HO potentials [53,54].…”

Section: Introductionmentioning

confidence: 99%

A quantum Monte Carlo study of confined quantum systems: application to harmonic oscillator and hydrogenic-like atoms

Barbosa

Almeida

Prudente

2015

J. Phys. B: At. Mol. Opt. Phys.

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The correlation function quantum Monte Carlo (CFQMC) approach is employed to study the energy spectra of confined quantum systems. This method, applied originally to determine rovibrational eigenenergies of molecules, is utilized here to calculate the energy levels of hydrogen atom, helium cation, lithium dication and two confined harmonic oscillator (HO) models: the one-dimensional HO within a box of impenetrable walls and the three-dimensional one confined by an impenetrable spherical box. The dependence of the eigenenergies on functional form and the number of the basis functions are analyzed for various confinement parameters. The present results are compared with those previously published, and the efficiency of the CFQMC method to treat confined quantum systems is discussed.

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A study of the confined 2D isotropic harmonic oscillator in terms of the annihilation and creation operators and the infinitesimal operators of the SU(2) group

Cited by 11 publications

References 23 publications

States of a hydrogen atom in an impenetrable cubic cavity

States of a hydrogen atom in an impenetrable cubic cavity

Information analysis in free and confined harmonic oscillator

A quantum Monte Carlo study of confined quantum systems: application to harmonic oscillator and hydrogenic-like atoms

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