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We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…
The derivative expansion of the one-loop effective action in QED$_3$ and QED$_4$ is considered. The first term in such an expansion is the effective action for a constant electromagnetic field. An explicit expression for the next term…
Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized…
The energy-based stochastic extension of the Schrodinger equation is perhaps the simplest mathematically rigourous and physically plausible model for the reduction of the wave function. In this article we apply a new simulation methodology…
Similarities between quantum systems and analogous systems for classical waves have been used to great effect in the physics community, be it to gain an intuition for quantum systems or to anticipate novel phenomena in classical waves. This…
Solutions of the time-dependent Schr\"odinger equation are mapped to other solutions for a (possibly) different potential by so-called form-preserving transformations. These time-dependent transformations of the space and time coordinates…
A simple example of especially constructed potential barrier enables to show analytically (not numerically) the existence of tunneling effect for a Sommerfeld particle.
A one-dimensional Schr\"odinger equation with position-dependent effective mass in the kinetic energy operator is studied in the framework of an $so(2,1)$ algebra. New mass-deformed versions of Scarf II, Morse and generalized…
This is the first paper in a series of three dealing with HS theories in flat spacetime. It is divided in three parts. The first part is an elaboration on the method of effective action, initiated in a previous paper. We study the…
Multi-time wave functions are wave functions that have a time variable for every particle, such as $\phi(t_1,x_1,\ldots,t_N,x_N)$. They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in…
In this letter, we consider a Schrodinger equation for a well potential with varying width. We solve one dimensional time-dependent Schrodinger equation subject to time-dependent boundary conditions for a spinless particle inside infinite…
The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods-Saxon potential reported in [Phys. Rev. C 72, 027001 (2005)] is extended to the fractional forms using the generalized fractional derivative…
A photon-like wavepacket based on novel solutions of Maxwell's equations is proposed. It is believed to be the first 'classical' model that contains so many of the accepted quantum features. In this new work, novel solutions to Maxwell's…
We present a new hydrodynamic analogy of nonrelativistic quantum particles in potential wells. Similarities between a real variant of the Schr\"odinger equation and gravity-capillary shallow water waves are reported and analyzed. We show…
It is often argued that measurable predictions of Bohmian mechanics cannot be distinguished from those of a theory with arbitrarily modified particle velocities satisfying the same equivariance equation. By considering the wave function of…
In this chapter we give a pedagogical introduction to effective potential methods in field theories. We first review the general functional methods leading to the concept of effective action and effective potential. Focusing on the…
Using the simplest but fundamental example, the problem of the infinite potential well, this paper makes an ideological attempt (supported by rigorous mathematical proofs) to approach the issue of…
F. Rohrlich has recently published two papers, including the paper under review, advocating a particular delay-differential equation as an approximate equation of motion for classical charged particles, which he characterizes as providing a…
Using classical statistics, Schrodinger equation in quantum mechanics is derived from complex space model. Phase-space probability amplitude, that can be defined on classical point of view, has connections to probability amplitude in…
Semiclassical expansion of the Wigner function for spin-1/2 fermions having an effective spacetime-dependent mass is used to analyze spin-polarization effects. The existing framework is reformulated to obtain a differential equation…