Related papers: Schroedinger Proof in Minplus Complex Analysis
The spinless Salpeter equation represents the simplest and most straightforward generalization of the Schroedinger equation of standard nonrelativistic quantum theory towards the inclusion of relativistic kinematics. Moreover, it can be…
We take up the idea of Nelson's stochastic processes, the aim of which was to deduce Schr\"odinger's equation. We make two major changes here. The first one is to consider deterministic processes which are pseudo-random but which have the…
We construct an explicit one-to-one correspondence between non-relativistic stochastic processes and solutions of the Schrodinger equation and between relativistic stochastic processes and solutions of the Klein-Gordon equation. The…
By application of the 'geometric spectral inversion' technique, which we have recently generalized to accommodate also singular interaction potentials, we construct from spectral data emerging from the solution of the Minkowski-space…
We show that the Schr\"odinger equation can be solved exactly based only on classical least action. Fundamental postulates of quantum mechanics can in turn be derived directly from this construction. The results extend to the relativistic…
By recursively solving the underlying Schr\" odinger equation, we set up an efficient systematic approach for deriving analytic expressions for discretized effective actions. With this we obtain discrete short-time propagators for both one…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
The analytical and numerical solutions of the Mathisson-Papapetrou equations under the Mathisson-Pirani supplementary condition describing highly relativistic (ultrarelativistic) motions of a spinning particle in a Schwarzschild field are…
The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
In this paper we propose an extended particle model whose evolution is deterministic. In dimension 2, the extended particle is represented by four points that define a small elastic string that vibrates, alternating between a creation…
We present a nonlinear stochastic Schroedinger equation for pure states describing non-Markovian diffusion of quantum trajectories. It provides an unravelling of the evolution of a quantum system coupled to a finite or infinite number of…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be…
This work presents a study on the nonrelativistic quantum motion of a charged particle in a rotating frame, considering the Aharonov-Bohm effect and a uniform magnetic field. We derive the equation of motion and the corresponding radial…
In quantum mechanics, the time evolution of particles is given by the Schr\"odinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not…
We formulate the Schr\"odinger equation as the equation of motion of a small external influence which serves as the initial boundary condition of a physical system in classical laboratory space. The Hilbert space of possible external…
It is shown that the generally covariant Duffin-Kemmer-Petiau equation, formulated in the frame of the Tetrode-Weyl-Fock-Ivanenko tetrad formalism, allows for a non-relativistic approximation if the metric tensor is of a special form. The…
This work investigates the motion of a non-relativistic charged particle within the spacetime of a global monopole. We introduce the Schr\"odinger equation to describe the particle's motion with two interactions by considering the Kratzer…
From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of…