Infrared Spectroscopy of Diatomic Molecules — A Fractional Calculus Approach

Herrmann, Richard

doi:10.1142/s0217979213500197

Cited by 11 publications

(7 citation statements)

References 28 publications

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“…Below α = 1/2 the fractional quantum harmonic oscillator using the Caputo derivative definition has no real eigenvalues any more. Based on the stationary fractional quantum harmonic oscillator the infrared spectrum of HCl has been reproduced successfully [32]. It has also been demonstrated, that the transition from vibrational (α ≈ 1) to rotational type (α ≈ 2) of spectra may be interpreted within the context of the fractional quantum harmonic oscillator as a transition from one-≈ 1 to three-dimensional ≈ 3 space, as long as the corresponding multiplicities are correctly implemented [32].…”

Section: Fractional Calculus With Time Dependent α In the Adiabatic Lmentioning

confidence: 95%

“…Since we consider the genesis of space as a quantum phenomenon, we describe this process with the simple model of the fractional quantum harmonic oscillator [32]:…”

Section: Fractional Calculus With Time Dependent α In the Adiabatic Lmentioning

confidence: 99%

“…We have already emphasized [32], that these levels allow for a smooth transition from vibrational to rotational types of spectra, depending on the value of the fractional derivative coefficient α. Indeed the solutions of the fractional quantum harmonic oscillator cover vibrational as well as rotational degrees of freedom from a generalized view as fractional vibrations [35].…”

Section: Fractional Calculus With Time Dependent α In the Adiabatic Lmentioning

confidence: 99%

“…We know, that the infrared spectra of diatomic molecules may be reproduced based on the level spectrum of the fractional quantum harmonic oscillator by defining the relative intensities I α as a Boltzmann distribution weighted with the degeneracy of the n-th energy level [32], where…”

Section: The Model and Possible Consequences For An Application In Comentioning

confidence: 99%

“…[32,35]. By the way, the explicit properties of the group elements and Casimir-operator for = 2 have not been investigated yet.…”

Section: The Model and Possible Consequences For An Application In Comentioning

confidence: 99%

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On the origin of space

Herrmann¹

2013

Open Physics

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Abstract:Within the framework of fractional calculus with variable order the evolution of space in the adiabatic limit is investigated. Based on the Caputo definition of a fractional derivative using the fractional quantum harmonic oscillator a model is presented, which describes space generation as a dynamic process, where the dimension of space evolves smoothly with time in the range 0 ≤ ( ) ≤ 3, where the lower and upper boundaries of dimension are derived from first principles. It is demonstrated, that a minimum threshold for the space dimension is necessary to establish an interaction with external probe particles. A possible application in cosmology is suggested.PACS (2008)

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Section: Fractional Calculus With Time Dependent α In the Adiabatic Lmentioning

confidence: 95%

“…Since we consider the genesis of space as a quantum phenomenon, we describe this process with the simple model of the fractional quantum harmonic oscillator [32]:…”

Section: Fractional Calculus With Time Dependent α In the Adiabatic Lmentioning

confidence: 99%

Section: Fractional Calculus With Time Dependent α In the Adiabatic Lmentioning

confidence: 99%

Section: The Model and Possible Consequences For An Application In Comentioning

confidence: 99%

“…[32,35]. By the way, the explicit properties of the group elements and Casimir-operator for = 2 have not been investigated yet.…”

Section: The Model and Possible Consequences For An Application In Comentioning

confidence: 99%

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On the origin of space

Herrmann¹

2013

Open Physics

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Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation

Medina

Núñez‐Zarur

Pérez-Torres

2019

Int J of Quantum Chemistry

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Nonadiabatic effects in the nuclear dynamics of the H2+ molecular ion, initiated by ionization of the H2 molecule, is studied by means of the probability and flux distribution functions arising from the space fractional Schrödinger equation. In order to solve the fractional Schrödinger eigenvalue equation, it is shown that the quantum Riesz fractional derivative operator fulfills the usual properties of the quantum momentum operator acting on the bra and ket vectors of the abstract Hilbert space. Then, the fractional Fourier grid Hamiltonian method is implemented and applied to molecular vibrations. The eigenenergies and eigenfunctions of the fractional Schrödinger equation describing the vibrational motion of the H2+ and D2+ molecules are analyzed. In particular, it is shown that the position‐momentum Heisenberg's uncertainty relationship holds independently of the fractional Schrödinger equation. Finally, the probability and flux distributions are presented, demonstrating the applicability of the fractional Schrödinger equation for taking into account nonadiabatic effects.

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Lie symmetry analysis and exact solution of certain fractional ordinary differential equations

Prakash

Sahadevan

2017

Nonlinear Dyn

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Infrared Spectroscopy of Diatomic Molecules — A Fractional Calculus Approach

Cited by 11 publications

References 28 publications

On the origin of space

On the origin of space

Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation

Lie symmetry analysis and exact solution of certain fractional ordinary differential equations

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