Related papers: The Potential Inversion Theorem
Evolution of a particle in an inverse square potential is studied. We derive an equation of motion for $\left<r^2\right>$ and solve it exactly. It gives us a possibility to identify the conditions under which a falling of a quantum particle…
It is known that the Schroedinger equation may be derived from a hydrodynamic model in which the Lagrangian position coordinates of a continuum of particles represent the quantum state. Using Routh\s method of ignorable coordinates it is…
The Schrodinger equation for stationary states in a central potential is studied in an arbitrary number of spatial dimensions, say q. After transformation into an equivalent equation, where the coefficient of the first derivative vanishes,…
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation…
We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain)…
In this and companion papers, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the quantization of electromagnetism permits the…
According to symmetrization postulate for a system of identical particles, wave function has to be completely symmetric or completely anti-symmetric. In this paper we want to mathematically justify this postulate ignoring the spin part of…
We consider a lattice model in which phonons scatter with pairs of electrons. All eigenvalues and eigenvectors can be obtained analytically. For a suitable choice of parameters the ground state consists of a Fermi sea of non-interacting…
We study the landscape of solutions of the coherent quantum states in a ring shaped lattice potential in the context of ultracold atoms with an effective positive nonlinearity induced by interatomic interactions. The exact analytical…
In solid state physics, it is an unsaid (tacit) assumption that the Bloch theorem is applicable to a crystal lattice even if it is of the macroscopic dimensions, provided periodicity is maintained. However, in a realistic situation,…
An effective theory of the excited states of positronium is derived and some of its consequences are explored. At large physical separation, the binding of the electron and positron is assumed to be described completely by QED, whereas all…
The assumption is made that only transversely polarized photons are needed for a correct description of Quantum Electrodynamics. A simple mathematical transformation is used to introduce new field operators which satisfy the full Maxwell…
Quantum electrodynamics near a boundary is investigated by considering the inertial mass shift of an electron near a dielectric or conducting surface. We show that in all tractable cases the shift can be written in terms of integrals over…
The present paper generalizes preceding papers of the author and opens a cycle of works concerning the general posing and solution in analytic form of the quantum-mechanical inverse scattering problem (for a given partial channel) in a…
A representation is put forward for wave functions of quantum particles in periodic lattice potentials subjected to homogeneous time-periodic forcing, based on an expansion with respect to Bloch-like states which embody both the spatial and…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
The Bloch theorem is a powerful theorem stating that the expectation value of the U(1) current operator averaged over the entire space vanishes in large quantum systems. The theorem applies to the ground state and to the thermal equilibrium…
We first recall that the system of fluid mechanics equations (Euler and continuity) that describes a fluid in irrotational motion subjected to a generalized quantum potential (in which the constant is no longer reduced to the standard…
A two-dimensional model of an electron moving under the influence of an attractive zero-range potential as well as external magnetic and electric fields is analyzed. We prove by numerical investigations that there are formed such resonances…