Related papers: Is the Bohr's quantization hypothesis necessary ?
A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to…
An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.
In this article and beginning with the Dirac solution to the Hydrogen atom in its ground state, the exact results corresponding to the expectation value of the distance of the electron to the proton and the maximum probability distance are…
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…
It is shown that when the gauge-invariant Bohr-Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field interpreted as operators then, in the…
It is shown that the momentum density of free electromagnetic field splits into two parts. One has no contribution to the net momentum due to the transversality condition. The other yields all the momentum. The angular momentum that…
We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field,…
Many structures in nature are invariant under the transformation (p,r)->(br,-p/b), where b is some scale factor. Born's reciprocity hypothesis affirms that this invariance extends to the entire Hamiltonian and equations of motion. We…
As the simplest atom in nature, the hydrogen atom has been explored thoroughly from the perspective of non-relativistic quantum mechanics to relativistic quantum mechanics. Among the research on hydrogen atom, its energy level is the most…
It is argued that the gauge anomalies are only the artefacts of quantum field theory when certain subtleties are not taken into account. With the Berry's phase needed to satisfy certain boundary conditions of the generating path integral,…
Superconductors have often been described as `giant atoms'. The simplest description of atoms that heralded their quantum understanding was proposed by Bohr in 1913. The Bohr atom starts from some simple assumptions and deduces that the…
I revisit the reply of Bohr to Einstein. Bohr's assertion that there are no causes in atomic scale systems is, as a closer analysis reveals, not in line with the Copenhagen interpretation since it would contain a statement about reality.…
Whether gravity is quantized remains an open question. To shed light on this problem, various Gedankenexperiments have been proposed. One popular example is an interference experiment with a massive system that interacts gravitationally…
This is a brief reply to Goldstein's article on ``Quantum Theory Without Observers'' in Physics Today. It is pointed out that Bohm's pilot wave theory is successful only because it keeps Schr\"odinger's (exact) wave mechanics unchanged,…
The classical Maxwell--Born--Infeld field equations coupled with a Hamilton--Jacobi law of point charge motion are partially quantized by coupling the Hamilton-Jacobi phase function with an amplitude function, which combines with the phase…
Traditionally, the Planck constant $h$ makes its debut appearance in quantum physics textbooks in the context of the blackbody radiation law and subsequently as a fundamental ingredient of the physics of the photoelectric effect and the…
Based on standard perturbation theory, we present a full quantum derivation of the formula for the orbital magnetization in periodic systems. The derivation is generally valid for insulators with or without a Chern number, for metals at…
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…