Related papers: Re-Thinking Schroedinger Boundary Conditions: the …
We consider the motion of a non relativistic quantum particle in R^3 subject to n point interactions which are moving on given smooth trajectories. Due to the singular character of the time-dependent interaction, the corresponding…
This paper mainly addresses the strong unique continuation property for the electromagnetic Schr\"{o}dinger operator with complex-valued coefficients. Appropriate multipliers with physical backgrounds have been introduced to prove a priori…
This work deals with Schr\"odinger equations with quadratic and sub-quadratic Hamiltonians perturbed by a potential. In particular we shall focus on bounded, but not necessarily smooth perturbations. We shall give a representation of such…
This paper studies the two-spinor form of the Rarita-Schwinger potentials subject to local boundary conditions compatible with local supersymmetry. The massless Rarita-Schwinger field equations are studied in four-real-dimensional…
The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrodinger equation coupled to a Poisson equation determining the gravitational potential. This wave-mechanical representation…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
It is proposed that the Schrodinger equation for a free point particle has non-linear corrections which depend on the mass of the particle. It is assumed that the corrections become extremely small when the mass is much smaller or much…
Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…
How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with…
We consider Schr\"{o}dinger equations with linearly energy-depending potentials which are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under…
Physical systems may couple to other systems through variables that are not gauge invariant. When we split a gauge system into two subsystems, the gauge-invariant variables of the two subsystems have less information than the gauge…
We consider inverse problems for wave, heat and Schr\"odinger-type operators and corresponding spectral problems on domains of ${\bf R}^n$ and compact manifolds. Also, we study inverse problems where coefficients of partial differential…
The modeling of finite-extent semiconductor nanostructures that are embedded in a host material requires the numerical treatment of the boundary in a finite simulation domain. For the study of a self-assembled InAs dot embedded in GaAs,…
We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and…
This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron…
Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending.…
The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary…
The vacuum dependence on boundary conditions in quantum field theories is analysed from a very general viewpoint. From this perspective the renormalization prescriptions not only imply the renormalization of the couplings of the theory in…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
In this paper the problem of the gauge in a bound state calculation is discussed. In particular, in order to verify the gauge invariance in the energy levels expansion, some set of gauge invariant contributions are given.