Related papers: The Schroedinger equation as the time evolution of…
From classical stochastic equations of motion we derive the quantum Schr\"odinger equation. The derivation is carried out by assuming that the real and imaginary parts of the wave function $\phi$ are proportional to the coordinates and…
In this paper, three plausible axioms together with two definitions are employed to build an axiomatic framework, and then with the help of the Dirac formalism, it is demonstrated that the time-dependent Schr\"odinger wave equation is no…
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 construct a local in time, exponentially decaying solution of the one-dimensional variable coefficient Schrodinger equation by solving a nonstandard boundary value problem. A main ingredient in the proof is a new commutator estimate…
Students in a quantum mechanics course are often introduced to the Schr\"odinger equation as the standard mathematical tool. However, rarely do students develop an understanding as to why the equation is the choice for modeling quantum…
We present a definition of integrability for the one dimensional Schroedinger equation, which encompasses all known integrable systems, i.e. systems for which the spectrum can be explicitly computed. For this, we introduce the class of…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
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…
We present some lower bounds for regular solutions of Schr\"odinger equations with bounded and time dependent complex potentials. Assuming that the solution has some positive mass at time zero within a ball of certain radius, we prove that…
Consider the cubic nonlinear Schr\"odinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the…
We illustrate a simple derivation of the Schrodinger equation, which requires only knowledge of the electromagnetic wave equation and the basics of Einstein's special theory of relativity. We do this by extending the wave equation for…
In this paper we introduce the use of Sylvester's formula for systems with degenerate eigenvalues in relation to obtaining their analytical solutions. To appreciate the use we include two other forms of analytical solutions namely adiabatic…
The macro-objectivation problem derives from the fact that the Schrodinger equation is linear and thus requires that a macroscopic system interacting with an entangled state must be entangled as well. However, such a requirement entails…
Using an explicit Euler substitution it was obtained a system of differential equations, which can be used to find the solution of time-dependent 1-dimentional Schr\H{o}dinger equation for a general form of the time-dependent potential.
We generalize the Lewis-Riesenfeld technique of solving the time-dependent Schrodinger equation to cases where the invariant has continuous eigenvalues. An explicit formula for a generalized Lewis-Riesenfeld phase is derived in terms of the…
We show that the time-dependent Schr\"odinger equation (TDSE) is the phenomenological dynamical law of evolution unraveled in the classical limit from a timeless formulation in terms of probability amplitudes conditioned by the values of…
Within Bohm`s interpretation of quantum mechanics particles follow classical trajectories that are determined by the full solution of the time dependent Schroedinger equation. If this interpretation is consistent it must be possible to…
We study the relation between two evolution pictures that are currently considered for totally constrained theories. Both descriptions are based on Rovelli's evolving constants approach, where one identifies a (possibly local) degree of…
Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an…
In this paper we deal with a nonlinear Schr\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time…