Eigenspectrum properties of the confined 3D harmonic oscillator

Stevanović, Lj.; Sen, K. D.

doi:10.1088/0953-4075/41/22/225002

Cited by 15 publications

(11 citation statements)

References 38 publications

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“…ω is the frequency of the oscillator and controls the potential strength. Analytic solutions for this Hamiltonian are for

n

even,

ψ_{n} (x) = A_{n} e^{- x^{2} / 2}_{1} F_{1} (\frac{1}{4} - \frac{E_{n}}{2}, \frac{1}{2}, x^{2})

and for

n

odd,

ψ_{n} (x) = B_{n} e^{- x^{2} / 2}_{1} F_{1} (\frac{3}{4} - \frac{E_{n}}{2}, \frac{3}{2}, x^{2}),

where

A_{n}

and

B_{n}

are normalization constants and

_{1} F_{1} (a, b, x)

is the Kummer confluent hypergeometric function.

E_{n}

are the energy eigenvalues.…”

Section: The Confined Harmonic Oscillatormentioning

confidence: 99%

“…In particular, the one dimensional confined Harmonic Oscillator model (cHO) has been studied in connection with issues such as the effect of distant boundaries on the energy levels , its effect on the separation of variables , the behavior of neutrons in atomic nuclei , the energies and the Einstein coefficients , and information entropies in position space . There are also interesting analyses on the features of the model in higher dimensions . Although there is a lot of work on these models and systems, there is significantly less work on their momentum representations as compared with the position‐space ones, and even less on their phase‐space representations.…”

Section: Introductionmentioning

confidence: 99%

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Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Laguna

Sagar

2014

Annalen der Physik

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Quantum uncertainties in position, momentum and phasespace are studied in the confined Harmonic Oscillator. Standard deviations and Shannon entropies are used to quantify these uncertainties and their behaviors are compared and contrasted. We observe a minimum in the momentum space Shannon entropy as the box length is increased, a feature that is not present in the momentum space standard deviation. The behaviors of the standard deviation product and the Shannon entropy sum, which form the basis of uncertainty relationships, are also analyzed. Maxima are observed in the product as the box length increases in sharp contrast to the entropy sum. The relationship between these behaviors and that of the Shannon entropy of the phase-space Wigner function is analyzed and discussed. An analysis of the energetic components is also performed. The results reinforce the idea that the confined Harmonic Oscillator can be considered as an intermediate model which interpolates between the Particle in a Box Model and the Harmonic Oscillator and thus contains characteristics of both models.

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“…ω is the frequency of the oscillator and controls the potential strength. Analytic solutions for this Hamiltonian are for

n

even,

ψ_{n} (x) = A_{n} e^{- x^{2} / 2}_{1} F_{1} (\frac{1}{4} - \frac{E_{n}}{2}, \frac{1}{2}, x^{2})

and for

n

odd,

ψ_{n} (x) = B_{n} e^{- x^{2} / 2}_{1} F_{1} (\frac{3}{4} - \frac{E_{n}}{2}, \frac{3}{2}, x^{2}),

where

A_{n}

and

B_{n}

are normalization constants and

_{1} F_{1} (a, b, x)

is the Kummer confluent hypergeometric function.

E_{n}

are the energy eigenvalues.…”

Section: The Confined Harmonic Oscillatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Laguna

Sagar

2014

Annalen der Physik

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“…For a hydrogen like atom with a nucleus in the center of a spherically sym metric cavity, almost exact estimates of it energy, polarizability [6,7], oscillator strengths [4,[8][9][10], and other properties [1-3, 9, 11] can be made. For similar problems with a harmonic oscillator in a cavity, see, e.g., [3,[12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Spectroscopic characteristics of simple systems in a spherical cavity

Пупышев

Stepanov

2014

Russ. J. Phys. Chem.

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Trends in the changes in the characteristics of spectral transitions of the simplest one electron sys tems (atoms, oscillators) in an impenetrable spherical cavity upon changing the parameters and size of a system are discussed. Methods for the qualitative analysis of changes in the characteristics of transitions are developed by analyzing the changes in electronic distributions and through the use of scale transformations.

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“…Quantum mechanical bounded oscillator was studied earlier in detail in the Refs. [29][30][31]. Main motivation for the study of network of quantum harmonic oscillators comes from their potential applications in the physics of conducting polymers, where polymer chain (e.g., in polyacetylene) can be considered as a branched structure, where lattice of the chain forms graph.…”

Section: Introductionmentioning

confidence: 99%