The analysis of rovibrational motion equations of a diatomic molecule in the linear regime

Jahanpanah, J.; Khoeini-Moghaddam, Salomeh

doi:10.1080/00268976.2017.1340683

Cited by 2 publications

(2 citation statements)

References 20 publications

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“…A heuristics model is introduced for constructing the vibrational Hamiltonian of a two-particle system in quantum mechanics. This model has already been implemented to form the vibrational [7] and rovibrational [23] Hamiltonians of diatomic molecules. Here, the vibrational Hamiltonian of Hydrogen-like atoms (5) has similarly defined as an infinite positive power series.…”

Section: Discussionmentioning

confidence: 99%

The forming mechanism of spontaneous emission noise flux radiated from hydrogen-like atoms by means of vibrational Hamiltonian

Jahanpanah

2021

AIP Advances

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A theoretical model is introduced for constructing the vibrational Hamiltonian of Hydrogenlike atoms (HLA). The Hamiltonian is then used to derive the vibrational motion equations of HLA in Heisenberg picture. The Langevin equation will ultimately be formed after adding the dissipative term and fluctuating (Langevin) force according to the fluctuation-dissipation theorem (FDT). The positional noise flux is then defined as the correlation function of fluctuations that happens for the electron position during its rather fast vibrational oscillations ( Hz vib 15 10   ). On the other hand, the positional fluctuations led to the fluctuations in the potential and kinetic energies of oscillating electron so that the appearance of the potential and kinetic noise fluxes is vulnerable. The positional, potential, and kinetic noise fluxes of oscillating electron will be determined by solving the Langevin equation in frequency domain.It is finally demonstrated that the potential and kinetic noise fluxes commonly act as an internal source for producing the external noise flux emitted from HLA in the form of spontaneous emission with a Lorentzian profile. In contrast with all previous procedures, no ambient effect has been involved to describe the forming mechanism of spontaneous emission for the first time.

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Section: Discussionmentioning

confidence: 99%

The forming mechanism of spontaneous emission noise flux radiated from hydrogen-like atoms by means of vibrational Hamiltonian

Jahanpanah

2021

AIP Advances

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“…Accordingly, the relativistic energy eigenvalue

E_{italicvib}^{italicrel}

is derived by applying the principles of special relativity to the kinetic and potential energies of the electron. The RVH,

H_{italicvib}^{italicrel}

, is then constructed by substituting the number operator

\overset{truê}{N}

for the energy level

n

in the relativistic energy eigenvalue

E_{italicvib}^{italicrel}

with a similar approach to derive energy eigenvalue of a simple harmonic oscillator

E_{n} = (n + 1 / 2) ℏ ω_{0}

that is directly converted into the Hamiltonian

{\overset{H}{true}}_{0} = (\overset{truê}{N} + 1 / 2) ℏ ω_{0}

[13, 17]. In these calculations,

ω_{0}

is the natural frequency of harmonic oscillator that has been introduced by Equation () of Reference [13] as

ω_{italicvib}^{((), 1)} = ω_{0} = {normalℏ}^{- 1} μ c^{2} {((), zα)}^{2}

(

μ \approx m_{e}

) for nonrelativistic electron oscillations.…”

Section: Introductionmentioning

confidence: 99%

Relativistic ro‐vibrational feature of electron in Bohr's orbits of hydrogen‐like atoms in Heisenberg picture

Jahanpanah

Vahedi

Khosrojerdi

2022

Int J of Quantum Chemistry

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The relativistic effects have been widely reported to affect the chemical and physical properties of the heavy elements such as lanthanides (57≤z≤71), actinides (89≤z≤103), and transactinides (z≥104). This effect is definitely weakened by reducing the atomic number z in lighter elements such as hydrogen‐like atoms (HLAs). The aim of present paper is to investigate the relativistic effects of electron motion in Bohr orbits on the chemical and physical properties of HLAs. The theoretical model is based on the Heisenberg (rather than Schrodinger) picture where the relativistic vibrational Hamiltonian (RVH) Hitalicvibitalicrel is expanded as a power series of harmonic oscillator Hamiltonian H0 for the first time. By applying the first‐order RVH (correct to H0) to the Heisenberg equation, a pair of coupled equations is obtained for the relativistic position and linear momentum of electron. A simple comparison of the first‐order relativistic and nonrelativistic equations reveals that the relativistic natural frequency of an HLA (like entropy) is slowly raised by increasing z beyond z≈20. In general, RVH plays a fundamental role because it specifies the temporal relativistic variations of position, velocity, and linear momentum of the oscillating electron. The results are finally verified by demonstrating energy conservation.

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The analysis of rovibrational motion equations of a diatomic molecule in the linear regime

Cited by 2 publications

References 20 publications

The forming mechanism of spontaneous emission noise flux radiated from hydrogen-like atoms by means of vibrational Hamiltonian

The forming mechanism of spontaneous emission noise flux radiated from hydrogen-like atoms by means of vibrational Hamiltonian

Relativistic ro‐vibrational feature of electron in Bohr's orbits of hydrogen‐like atoms in Heisenberg picture

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