The hydrogen atom with the Coulomb interaction is one of the exactly solvable non-relativistic quantum models. Unlike many other exactly solvable models it describes a real physical object providing the formulas for energy levels and stationary state wave functions of a real hydrogen atom. In this paper we modify the model replacing the Coulomb interaction by the interaction of the proton and the electron with the classical electromagnetic field serving as an intermediary transmitting the electromagnetic interaction of these two charged quantum particles.The hydrogen atom with the Coulomb interaction is one of the exactly solvable non-relativistic quantum models. Unlike many other exactly solvable models it describes a real physical object providing the formulas for energy levels and stationary state wave functions of a real hydrogen atom. In this paper we modify the model replacing the Coulomb interaction by the interaction of the proton and the electron with the classical electromagnetic field serving as an intermediary transmitting the electromagnetic interaction of these two charged quantum particles.

arXiv:1308.0221Aug 1, 20130 citations

The hydrogen atom revisited

Randell L Mills

International Journal of Hydrogen EnergyDec 1, 200056 citations

Interaction of the hydrogen molecule with the environment: stability of the system

Izabela A. Wrona, M.W. Jarosik, Radosław Szczȩśniak +3 more

We study the stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme. We determined the properties of the molecule taking into account all electronic interactions, where the parameters of the Hamiltonian have been computed by using the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically ( $γ$ ) with the help of the non-hermitian operator. We have shown that the hydrogen molecule is dynamically unstable. The dissociation time ( $T_{D}$ ) decreases, if the $γ$ parameter increases (for $γ\rightarrow 0$ , we get $T_{D}\rightarrow +\infty$ ). At the dynamic instability of the hydrogen molecule overlaps its static instability as the coupling constant $γ$ increases. We observed the decrease in the dissociation energy and the existence of the metastable state of the molecule ( $γ_{MS}=0.659374$ ~Ry). The hydrogen molecule is statically unstable for $γ>γ_{D}=1.024638$ ~Ry. One can also observed the $\mathcal{PT}$ symmetry breaking effect for the electronic Hamiltonian ( $γ_{\mathcal {PT}}=0.520873$ ~Ry). However, it does not affect the properties of the hydrogen molecule, such as: the electronic Hamiltonian parameters, the phonon and rotational energy, and the values of the electron-phonon coupling constants.We study the stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme. We determined the properties of the molecule taking into account all electronic interactions, where the parameters of the Hamiltonian have been computed by using the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically ($γ$) with the help of the non-hermitian operator. We have shown that the hydrogen molecule is dynamically unstable. The dissociation time ($T_{D}$) decreases, if the $γ$ parameter increases (for $γ\rightarrow 0$, we get $T_{D}\rightarrow +\infty$). At the dynamic instability of the hydrogen molecule overlaps its static instability as the coupling constant $γ$ increases. We observed the decrease in the dissociation energy and the existence of the metastable state of the molecule ($γ_{MS}=0.659374$~Ry). The hydrogen molecule is statically unstable for $γ>γ_{D}=1.024638$~Ry. One can also observed the $\mathcal{PT}$ symmetry breaking effect for the electronic Hamiltonian ($γ_{\mathcal {PT}}=0.520873$~Ry). However, it does not affect the properties of the hydrogen molecule, such as: the electronic Hamiltonian parameters, the phonon and rotational energy, and the values of the electron-phonon coupling constants.

arXiv:1902.10520Jan 13, 20190 citations

γ

) with the help of the non-hermitian operator. We have shown that the hydrogen molecule is dynamically unstable. The dissociation time (

T_{D}

) decreases, if the

γ

parameter increases (for

γ\rightarrow 0

, we get

T_{D}\rightarrow +\infty

). At the dynamic instability of the hydrogen molecule overlaps its static instability as the coupling constant

γ

increases. We observed the decrease in the dissociation energy and the existence of the metastable state of the molecule (

γ_{MS}=0.659374

~Ry). The hydrogen molecule is statically unstable for

γ>γ_{D}=1.024638

~Ry. One can also observed the

\mathcal{PT}

symmetry breaking effect for the electronic Hamiltonian (

γ_{\mathcal {PT}}=0.520873

~Ry). However, it does not affect the properties of the hydrogen molecule, such as: the electronic Hamiltonian parameters, the phonon and rotational energy, and the values of the electron-phonon coupling constants.