Related papers: Re-Thinking Schroedinger Boundary Conditions: the …
We discuss the relationship between the boundary conditions of the Schwinger-Dyson equations and the phase diagram of a bosonic field theory or matrix model. In the thermodynamic limit, many boundary conditions lead to the same solution,…
It is known that the Schroedinger equation is not covariant under Galilei boosts, unless the phase of its solutions are shifted simultaneously. It is argued that the phase shift is not a coordinate transformation, because it depends on the…
With a choice of boundary conditions for solutions of the Schr\"odinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts…
We re-examine the justification for the imposition of regular boundary conditions on the wavefunction at the Coulomb singularity in the treatment of the hydrogen atom in non-relativistic quantum mechanics. We show that the issue of the…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
We study admissible boundary conditions for a charged quantum particle in a two-dimensional region subjected to an external magnetic field, i.e. a quantum magnetic billiard. After reviewing some physically interesting classes of admissible…
A key point in the spin foam approach to quantum gravity is the implementation of simplicity constraints in the partition functions of the models. Here, we discuss the imposition of these constraints in a phase space setting corresponding…
In this article we continue our investigations of one particle quantum scattering theory for Schroedinger operators on a set of connected (idealized one-dimensional) wires forming a graph with an arbitrary number of open ends. The…
A first-order gauge invariant formulation for the two-dimensional quantum rigid rotor is long known in the theoretical physics community as an isolated peculiar model. Parallel to that fact, the longstanding constraints abelianization…
In physical theories, boundary or initial conditions play the role of selecting special situations which can be described by a theory with its general laws. Cosmology has long been suspected to be different in that its fundamental theory…
We consider a statistical ensemble of particles of mass m, which can be described by a probability density \rho and a probability current \vec{j} of the form \rho \nabla S/m. The continuity equation for \rho and \vec{j} implies a first…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
The nonlinear Schrodinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is…
Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the…
The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A new formulation of constraint-preserving boundary conditions of…
Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
The stationary nonlinear Schroedinger equation, or Gross-Pitaevskii equation, is studied for the cases of a single delta potential and a delta-shell potential. These model systems allow analytical solutions, and thus provide useful insight…
In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the behaviour of a function on the boundary and in the interior. Additionally, boundary values can appear as additive…
Interior-boundary conditions (IBCs) are boundary conditions on wave functions for Schr\"odinger equations that allow that probability can flow into (and thus be lost at) a boundary of configuration space while getting added in another part…