In this paper, continuing the successful application of the Flow Theory of Hybrid Distributions to the quantum harmonic oscillator and Bose-Einstein Condensates (BEC), the formalism is extended to the description of hydrogen atom stationary states and radiative processes. By abandoning complex-valued wave functions and orthodox Schrodinger boundary conditions, the atomic levels are analyzed within the dual time-duration-energy (𝐸, 𝜏) manifold [1,2]. It is demonstrated that stationary states emerge naturally as dynamically stable phase-space solitons when kinetic dispersion along the duration axis (playing the role of temporal inertia) and nonlinear KramersMoyal (K-M) phase compression perfectly counterbalance stochastic vacuum diffusion [3,4,5]. By coupling the K-M kinetics coefficients with Einstein's radiation theory [7], spontaneous emission (coefficient A) is analytically derived from the first-order vacuum friction (gamma), while stimulated emission and absorption (coefficients 𝐵21and 𝐵12) are derived from the second-order field-modulated diffusion (B). Upon isolating the diffusion coefficient, its strict dependence on the fifth power of the orbital frequency (𝜔5) is uncovered. This fundamental nonlinearity opens up new predictive elements: nonlinear quantum chaos suppression in Rydberg atoms [8] and a natural asymmetry of spectral line profiles in the vacuum, providing directly experimentally verifiable predictions for Rydberg atom spectroscopy.In this paper, continuing the successful application of the Flow Theory of Hybrid Distributions to the quantum harmonic oscillator and Bose-Einstein Condensates (BEC), the formalism is extended to the description of hydrogen atom stationary states and radiative processes. By abandoning complex-valued wave functions and orthodox Schrodinger boundary conditions, the atomic levels are analyzed within the dual time-duration-energy (𝐸, 𝜏) manifold [1,2]. It is demonstrated that stationary states emerge naturally as dynamically stable phase-space solitons when kinetic dispersion along the duration axis (playing the role of temporal inertia) and nonlinear KramersMoyal (K-M) phase compression perfectly counterbalance stochastic vacuum diffusion [3,4,5]. By coupling the K-M kinetics coefficients with Einstein's radiation theory [7], spontaneous emission (coefficient A) is analytically derived from the first-order vacuum friction (gamma), while stimulated emission and absorption (coefficients 𝐵21and 𝐵12) are derived from the second-order field-modulated diffusion (B). Upon isolating the diffusion coefficient, its strict dependence on the fifth power of the orbital frequency (𝜔5) is uncovered. This fundamental nonlinearity opens up new predictive elements: nonlinear quantum chaos suppression in Rydberg atoms [8] and a natural asymmetry of spectral line profiles in the vacuum, providing directly experimentally verifiable predictions for Rydberg atom spectroscopy.

Jun 28, 20260 citations

Radiation emission by an atom in an external electromagnetic field

A. P. Kazantsev

Apr 1, 19740 citations

Two-frequency excitation of hydrogen atoms

P. Stehle

When a hydrogen atom in a state with principal quantum number ${n}_{i}$ is irradiated simultaneously with light of frequency ${\ensuremath{\omega}}_{L}$, nearly that required to produce a transition to a higher state with principal quantum number ${n}_{f}$ and with microwave radiation of frequency $\ensuremath{\omega}$, the transition is very probable when the resonance condition ${\ensuremath{\omega}}_{L}+k\ensuremath{\omega}={E}_{f}\ensuremath{-}{E}_{i}$ is satisfied, the emission or absorption of the net number $k$ of microwave photons just compensating for the detuning of the light from the resonance. This process is analyzed with the use of a forward scattering method and the results are used to discuss the experiments of Bayfield et al. on the excitation of hydrogen.When a hydrogen atom in a state with principal quantum number ${n}_{i}$ is irradiated simultaneously with light of frequency ${\ensuremath{\omega}}_{L}$, nearly that required to produce a transition to a higher state with principal quantum number ${n}_{f}$ and with microwave radiation of frequency $\ensuremath{\omega}$, the transition is very probable when the resonance condition ${\ensuremath{\omega}}_{L}+k\ensuremath{\omega}={E}_{f}\ensuremath{-}{E}_{i}$ is satisfied, the emission or absorption of the net number $k$ of microwave photons just compensating for the detuning of the light from the resonance. This process is analyzed with the use of a forward scattering method and the results are used to discuss the experiments of Bayfield et al. on the excitation of hydrogen.

Physical Review ANov 1, 19824 citations

Excitation of atomic hydrogen

S. N. Tiwary, D. D. Singh

Unknown eBooksJul 1, 19920 citations

Electronic transitions between energy levels without the emission of electromagnetic radiation

Emory Taylor, Rajan N. Iyer

In a previous paper, it was explained that the absorption and emission process (AE-process) of Bohr’s model of the hydrogen atom must involve an electric charge (i.e., electron) transiting between atomic energy levels instead of quantum jumping; otherwise, there is no way to use the AE-process to predict the fine structure constant. In this paper, it is shown that (1) a complete oscillation of the atomic electron (i.e., an electric charge) and of the induced magnetic field must occur for Bohr’s hydrogen atom to emit electromagnetic radiation, and (2) an atomic electron (i.e., electric charge) of Bohr’s hydrogen atom can transit between energy levels without the atom emitting electromagnetic radiation.In a previous paper, it was explained that the absorption and emission process (AE-process) of Bohr’s model of the hydrogen atom must involve an electric charge (i.e., electron) transiting between atomic energy levels instead of quantum jumping; otherwise, there is no way to use the AE-process to predict the fine structure constant. In this paper, it is shown that (1) a complete oscillation of the atomic electron (i.e., an electric charge) and of the induced magnetic field must occur for Bohr’s hydrogen atom to emit electromagnetic radiation, and (2) an atomic electron (i.e., electric charge) of Bohr’s hydrogen atom can transit between energy levels without the atom emitting electromagnetic radiation.

Physics EssaysDec 5, 20235 citations

When a hydrogen atom in a state with principal quantum number

{n}_{i}

is irradiated simultaneously with light of frequency ${\ensuremath{\omega}}_{L}$, nearly that required to produce a transition to a higher state with principal quantum number

{n}_{f}

and with microwave radiation of frequency $\ensuremath{\omega}$, the transition is very probable when the resonance condition ${\ensuremath{\omega}}_{L}+k\ensuremath{\omega}={E}_{f}\ensuremath{-}{E}_{i}$ is satisfied, the emission or absorption of the net number

k

of microwave photons just compensating for the detuning of the light from the resonance. This process is analyzed with the use of a forward scattering method and the results are used to discuss the experiments of Bayfield et al. on the excitation of hydrogen.