Related papers: The "Sommerfeld Puzzle" and Its Extensions

Using elements of symmetry, as gauge invariance, several aspects of a Schr\"odinger equation represented in phase-space are introduced and analyzed under physical basis. The Hydrogen atom is explored in the same context. Then we add a…

We extend the well-known Sacks-Uhlenbeck energy gap result (1981) for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic…

A framework is suggested in which the energy integrals of the Friedmann cosmology are identified as genuine time-independent physical characteristics for both vacuum and non-vacuum forms of cosmic energy. The integrals are found to be…

Left unnoticed for almost a century, 1916 Sommerfeld H theory hides a van der Waals-Maxwell phase transition in the Coulomb lepton-nucleon attraction of ground state H. This classical 19th century symmetry breaking effect, important for…

In 1927 Heisenberg discovered that the ``more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa''. Four years later G\"odel showed that a finitely specified, consistent formal…

Using the China unitary principle to test the Dirac theoryfor the hydrogen atomic spectrum shows that the standard Dirac function withthe Dirac energy levels is only one the formal solutions of theDirac-Coulomb equation, which conceals some…

We derive some properties of the hydrogen atom inside a box with an impenetrable wall that have not been discussed before. Suitable scaling of the Hamiltonian operator proves to be useful for the derivation of some general properties of the…

In this paper we determine in second order in the fine structure constant the energy levels of Weber's Hamiltonian admitting a quantized torus. Our formula coincides with the formula obtained by Wesley using the Schr\"odinger equation for…

Bohr and Rosenfeld carried out an analysis of the consequences of field theory commutation relations. In this note the analysis is sharpened. A conjecture of Heisenberg that volume is quantized is shown to be a consequence of the second…

The two-dimensional hydrogen-like atom in a constant magnetic field is considered. It is found that this is actually two separate problems. One for which the magnetic field causes an effective attraction between the nucleus and the electron…

Recently it was shown that classical "relativistic" particle dynamics was implicit in physics going back to Maxwell. The demonstration utilized a simple modification of a 1906 thought experiment by which Einstein established the mass…

For the hydrogen atom in combined magnetic and electric fields we investigate the dependence of the quantum spectra, classical dynamics, and statistical distributions of energy levels on the mutual orientation of the two external fields.…

The tight connection between mass and energy unveiled by Special Relativity, summarized by the iconic formula $E = mc^2$, has revolutionized our understanding of nature and even shaped our political world over the past century through its…

We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the…

A tautological system, introduced in [16][17], arises as a regular holonomic system of partial differential equations that govern the period integrals of a family of complete intersections in a complex manifold $X$, equipped with a suitable…

A two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections…

Recently, we have presented some simple arguments supporting the existence of certain complementarity between thermodynamic quantities of temperature and energy, an idea suggested by Bohr and Heinsenberg in the early days of Quantum…

A hierarchical ordering is demonstrated for the periodic orbits in a strongly coupled multidimensional Hamiltonian system, namely the hydrogen atom in crossed electric and magnetic fields. It mirrors the hierarchy of broken resonant tori…

For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom…

Employing a relativistic version of a hypervirial result, recurrence relations for arbitrary non-diagonal radial hydrogenic matrix elements have recently been obtained in Dirac relativistic quantum mechanics. In this contribution honoring…