Related papers: The Potential Inversion Theorem
In this paper, we study electron wavepacket dynamics in electric and magnetic fields. We rigorously derive the semiclassical equations of electron dynamics in electric and magnetic fields. We do it both for free electron and electron in a…
The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but…
In this paper, we show that the quantum bound state problems are mapped to $N$ point vortices with the identical circulation or strength using the Steiljes electrostatic model with imaginary charges. We also show that these $N$ point…
We study the symmetric periodic Anderson model of the conduction electrons hybridized with the localized correlated electrons on square lattice. Using the canonical representation of electrons by Kumar, we do a self-consistent theory of its…
A model of spontaneous wavefunction collapse, which is explicitly local and Lorentz-invariant, is defined. Some of the predictions of the model for specific experimental situations are derived. It is shown that, although incompatible…
Maxwell-Lorenz theory describes only vortex electromagnetic processes. Potential component of the magnetic field is usually excluded by the introduction of mathematical terms: Coulomb and Lorenz gauges. Proposed approach to the construction…
In this paper we consider a class of logarithmic Schr\"{o}dinger equations with a potential which may change sign. When the potential is coercive, we obtain infinitely many solutions by adapting some arguments of the Fountain theorem, and…
Rotation of atoms in a lattice is studied using a Hubbard model. It is found that the atoms are still contained in the trap even when the rotation frequency is larger than the trapping frequency. This is very different from the behavior in…
We investigate the dynamics of two bosons trapped in an infinite one-dimensional optical lattice potential within the framework of the Bose-Hubbard model and derive an exact expression for the wavefunction at finite time. As initial…
Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the…
Non-perturbatively generated effective potentials play an extremely useful and often critical role in string and inflationary model building. These potentials are typically computed by methods that assume the system is in equilibrium. For…
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…
We explore the phenomenon of emergent Lorentz invariance in strongly coupled theories. The strong dynamics is handled using the gauge/gravity correspondence. We analyze how the renormalization group flow towards Lorentz invariance is…
The concept of partnership of potentials is studied in detail and in particular the non-uniqueness due to the ambiguity in the election of the factorization energy and in the choice of the solution of certain Riccati equation. We generate…
We prove a logarithmic stability estimate for the inverse problem of determining the potential in a wave equation from boundary measurements obtained by varying the first component of the initial condition. The novelty of the present work…
Supersymmetric Quantum Mechanics may be used to construct reflectionless potentials and phase-equivalent potentials. The exactly solvable case of the $\lambda sech^2$ potential is used to show that for certain values of the strength…
We develop a general mapping from given kink or pulse shaped travelling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping - by definition an…
The theoretical foundations of quantum mechanics and de Broglie--Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal…
It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when…
In quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us…