Related papers: $SO(4)$ Symmetry in Hydrogen Atom with Spin
In this paper the N=2 supersymmetric extension of the Schroedinger Hamiltonian with 1/r-potential in arbitrary space-dimensions is constructed. The supersymmetric hydrogen atom admits a conserved Laplace-Runge-Lenz vector which extends the…
The fine structure of hydrogen energy was calculated by using the usual momentum-wavefunction relation directly, rather than establishing the well-known Dirac wave equation. As the results, the energy levels are completely the same as that…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
Consider the problem: why does the bound state spectrum $E(n) < 0$, of hydrogen atom Hamiltonian $H$ have more degenerate eigenstates than those required by rotational symmetry? The answer is well known and was demonstrated by Pauli. It is…
We study the hydrogen atom eigenstate energy and wave function in the Rindler space. The probability distribution is tilted because the electric field of the nucleus is no longer spherically symmetric. The hydrogen atom therefore cannot be…
For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this…
In this work, we study the modified Dirac equation in the framework of very special relativity (VSR). The low-energy regime is accessed and the nonrelativistic Hamiltonian is obtained. It turns out that this Hamiltonian is similar to that…
The three dimensional rotation group, SO(3), is a symmetry group of the normal hydrogen atom. Each reducible representation of this group can be associated with a degenerate energy level. If this atom is placed in an external magnetic…
The hydrogen atom is supposed to be described by a generalization of Schr\"{o}dinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential $r^{-\beta}$. Starting from previously obtained solutions…
The Bohm causal theory of quantum mechanics with spin-dependence is used to determine electron trajectories when a hydrogen atom is subjected to (semi-classical) radiation. The transition between the 1s ground state and the 2p0 state is…
We touch upon a long-standing question of the "true" one-dimensional hydrogen atom solution. From a symmetry point of view, Kepler problem in $d\ge2$ dimension is characterized by geometrical rotational symmetry, $SO(d)$, as well as…
A momentum representation treatment of the hydrogen atom problem with a generalized uncertainty relation,which leads to a minimal length ({\Delta}X_{i})_{min}= \hbar \sqrt(3{\beta}+{\beta}'), is presented. We show that the distance squared…
A two-dimensional hydrogen atom offers a promising alternative for describing the quantum interaction between an electron and a proton in the presence of a straight cosmic string. Reducing the hydrogen atom to two dimensions enhances its…
We revisit the quantum-mechanical two-dimensional hydrogen atom with an electric field confined to a circular box of impenetrable wall. In order to obtain the energy spectrum we resort to the Rayleigh-Ritz method with a polynomial basis…
We explore the fundamental but untested possibility that the photon is a continuous spin particle (CSP) with a small but non-zero spin Casimir $\rho$. When $\rho\neq 0$, the familiar polarization modes of the photon transform non-trivially…
The energy-momentum and spin tensors for a given theory can be replaced by alternative expressions that obey the same conservation laws for the energy, linear momentum, as well as angular momentum but, however, differ by the local…
The Dirac equation in the external Coulomb field is proved to possess the symmetry determined by the 31 operators, which form the 31-dimensional algebra. Two different fermionic realizations of the SO(1,3) algebra of the Lorentz group are…
When the hydrogen atom moves, the proton current generates a magnetic field which interacts with the hydrogen electron. A simple analyze shows that this interaction between the hydrogen momentum and the electron is of order of…
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the…
In 1905, Einstein formulated his special relativity for point particles. For those particles, his Lorentz covariance and energy-momentum relation are by now firmly established. How about the hydrogen atom? It is possible to perform Lorentz…