Related papers: Generalized Schrodinger Equation and Constructions…
In this work, we derive a generalization of the so-called Schr\"odinger-Langevin or Kostin equation for a Brownian particle interacting with a heat bath. This generalization is based on a nonlinear interaction model providing a…
The general solution of M\o ller's field equations in case of spherical symmetry is derived. The previously obtained solutions are verified as special cases of the general solution.
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum…
It is shown that any finitely generated subring of a global field has a universal first-order definition in its fraction field. This covers Koenigsmann's result for the ring of integers and its subsequent extensions to rings of integers in…
We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized…
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…
We discuss how basic notions of graph theory and associated graph polynomials define questions for algebraic geometry, with an emphasis given to an analysis of the structure of Feynman rules as determined by those graph polynomials as well…
Feynman's formulation of quantum theory is remarkable in its combination of formal simplicity and computational power. However, as a formulation of the abstract structure of quantum theory, it is incomplete as it does not account for most…
The usual formulations of quantum field theory in Minkowski spacetime make crucial use of Poincare symmetry, positivity of total energy, and the existence of a unique, Poincare invariant vacuum state. These and other key features of quantum…
Quantum technology is seeing a remarkable explosion in interest due to a wave of successful commercial technology. As a wider array of engineers and scientists are needed, it is time we rethink quantum educational paradigms. Current…
A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.
Quantum field theory offers physicists a tremendously wide range of application; it is both a language with which a vast variety of physical processes can be discussed and also it provides a model for fundamental physics, the so-called…
In this survey the contemporary results concerning supersymmetries in generalized Schr\"odinger equations are presented. Namely, position dependent mass Sch\"odinger equations are discussed as well as the equations with matrix potentials.…
The traditional, standard approach to quantum theory is to assume that the theory ``really'' contains only unitary physical dynamics--i.e., that the only physically quantifiable evolution is that given by the time-dependent Schrodinger…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
This is the second step of a program to use anharmonic plane waves as basis set in non-perturbative quantum field theory. The general framework developed previously is applied to quantum electrodynamics. To test the compatibility with…
We present a formalism based on the functional Schr\"odinger equation to analyse time-dependent tunneling in quantum field theory at the semi-classical level. The full problem is reduced step by step to a finite dimensional quantum…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
The ordinary quantum theory points out that general relativity is negligible for spatial distances up to the Planck scale. Consistency in the foundations of the quantum theory requires a``soft'' spacetime structure of the general relativity…