Related papers: Precanonical Quantization and the Schroedinger Wav…
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…
By defining a prepotential function for the stationary Schr\"odinger equation we derive an inversion formula for the space variable $x$ as a function of the wave-function $\psi$. The resulting equation is a Legendre transform that relates…
The normalisation relation between the bound and scattering S-state wave functions, extrapolated to the bound state pole, is derived from the Schroedinger equation. It is shown that, unlike previous work, the result does not depend on the…
The wave-function in quantum gravity is supposed to obey the Wheeler-DeWitt (WDW) equation, however there is neither a satisfactory probability interpretation nor a successful solution to the problem of time in the WDW framework. To gain…
Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the…
Time-continuous wavefunction collapse mechanisms n o t restricted to markovian approximation have been found only a few years ago, and have left many issues open. The results apply formally to the standard relativistic…
Both the additional non-linear term in the Schr\"odinger equation and the additional non-Hamiltonian term in the von Neumann equation, proposed to ensure localisation and decoherence of macro-objects, resp., contain the same Newtonian…
In flat spacetime, the Dirac equation is the "square root" of the Klein-Gordon equation in the sense that by applying the square of the Dirac operator to the Dirac spinor, one recovers the Klein-Gordon equation duplicated for each component…
The De Donder-Weyl (DW) Hamiltonian theory of fields treats space and time variables on equal footing. Its quantization, called precanonical quantization, leads to a hypercomplex generalization of quantum formalism to field theory as it…
In this paper we apply the formalism of the analytical signal theory to the Schrodinger wavefunction. Making use exclusively of the wave-particle duality and the principle of relativistic covariance, we actually derive the form of the…
The canonical quantization of $D=2n$ dimensional Dirac spinning particle in the external electromagnetic field is carried out in the gauge which allows to describe simultaneously particles and antiparticles (massive and massless) already at…
Using a new state-dependent, $\lambda$-deformable, linear functional operator, ${\cal Q}_{\psi}^{\lambda}$, which presents a natural $C^{\infty}$ deformation of quantization, we obtain a uniquely selected non--linear, integro--differential…
The classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and…
Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities, such as the vacuum current, are calculated the results are not gauge invariant. The non-gauge invariant terms have to be removed…
The functional Schrodinger equation is used to study the quantum collapse of a gravitating, spherical domain wall and a massless scalar field coupled to the metric. The approach includes backreaction of pre-Hawking radiation on the…
One of the main results of Scale Relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The Scale Relativity theory introduces an explicit dependence of…
By using the multipolar gauge it is shown that the quantum mechanics of an electrically charged particle moving in a prescribed classical electromagnetic field (wave mechanics) may be expressed in a manner that is gauge invariant, except…
The Eherenfest theorem states that Schrodinger representation of quantum mechanics (wave mechanics) reproduces Newton laws of motion in terms of expectation values. Remarkably, the contrary is considered elusive and, indeed, many authors…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
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…