Related papers: A Subtlety of the Schr\"{o}dinger Picture Dynamics
In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein-Gordon wavefunctions, as special cases; and then in turn for non-relativistic…
In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schr\"odinger operators whose potentials are obtained by real-valued sampling along the orbits of an ergodic invertible transformation. After an…
We study the quantum mechanics of the derivative nonlinear Schrodinger equation which has appeared in many areas of physics and is known to be classically integrable. We find that the N-body quantum problem is exactly solvable with both…
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…
Schroedinger's wave function shows many aspects of a state of incomplete knowledge or information ("bit"): (1) it is usually defined on a space of classical configurations, (2) its generic entanglement is, therefore, analogous to…
We present a systematic derivation of the wave kinetic equation describing the dynamics of a statistically inhomogeneous incoherent wave field in a medium with a weak quadratic nonlinearity. The medium can be nonstationary and…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
We study a class of quasi-linear Schr\"odinger equations arising in the theory of superfluid film in plasma physics. First, using gauge transforms and a derivation process we solve, under some regularity assumptions, the Cauchy problem.…
A striking feature of standard quantum mechanics is its analogy with classical fluid dynamics. In particular it is well known the Schr\"{o}dinger equation can be viewed as describing a classical compressible and non-viscous fluid, described…
In this paper, we study the nonrelativistic quantum mechanics of an electron in a spacetime containing a topological defect. We also consider that the electron is influenced by the Hulth\'{e}n potential. In particular, we deal with the…
An alternative method is proposed for deriving the time dependent Schroedinger equation from the pictures of wave and matrix mechanics. The derivation is of a mixed classical quantum character, since time is treated as a classical variable,…
In the present paper, first the mathematical basic properties of the exceptional points are discussed. Then, their role in the description of real physical quantum systems is considered. Most interesting value is the phase rigidity of the…
Atomic wave packets in optical lattices which are both spatially finite and time-dependent exhibit many striking similarities with light pulses in photonic crystals. We analytically characterize the transmission properties of such a…
Considering the recently established arbitrariness the Schroedinger equation has to be interpreted as an equation of motion for a statistical ensemble of particles. The statistical qualities of individual particles derive from the unknown…
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition…
The basic physical problems that necessitated the emergence of quantum physics are summarized, along with the elements of wave mechanics and its traditional statistical interpretation. Alternative interpretations to the statistical one,…
We consider the case of a cubic nonlinear Schr\"{o}dinger equation with an additional chaotic potential, in the sense that such a potential produces chaotic dynamics in classical mechanics. We derive and describe an appropriate…
We present a method to calculate exact dynamics of a wave-packet in a quantum two-state problem with Dirac delta coupling. The advantage of our method is that the calculations are done in the time domain. Hence inverting the solutions from…
The linear Schr\"{o}dinger equation does not predict that macroscopic bodies should be located at one place only. Quantum mechanics textbooks generally solve the problem by introducing the projection postulate, which forces definite values…
Classical mechanics for individual physical systems and quantum mechanics of non-relativistic particles are shown to be exceptional cases of a generalized dynamics described in terms of maps between two manifolds, the source being…