相关论文: Cornelius Lanczos -- Discoveries in the Quantum an…

Feynman's path integral formulation arose from his attempt to incorporate the Lagrangian framework into quantum mechanics, offering what he regarded as a more fundamental perspective than the Hamiltonian approach, particularly in the…

Considered one of the founding fathers of integral geometry, Luis Santal\'o has contributed to various areas of mathematics. His work has applications in number theory, in the theory of differential equations, in stochastic geometry, in…

Generalisations of the virial theorm in Classical Mechanics and Quantum Mechanics are examined. It is shown that the generalised virial theorem in Quantum Mechanics leads to certain relations between matrix elements. The differences between…

At the beginning of the previous century, Newtonian mechanics fell victim to two new revolutionary theories, Quantum Mechanics (QM) and General Relativity (GR). Both theories have transformed our view of physical phenomena, with QM…

The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…

Heisenberg's breakthrough in his July 1925 paper that set in motion the development of Quantum Mechanics through subsequent papers by Born, Jordan, Heisenberg and also Dirac (from 1925 to 1927) is reexamined through a modern lens. In this…

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the…

The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…

In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for…

Quantum mechanics, information theory, and relativity theory are the basic foundations of theoretical physics. The acquisition of information from a quantum system is the interface of classical and quantum physics. Essential tools for its…

The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…

Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the…

We report an implementation of the recursion method that addresses quantum many-body dynamics in the nonperturbative regime. The method essentially amounts to constructing a Lanczos basis in the space of operators and solving coupled…

Starting from the earlier notions of stationary action principles, we show how Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics.…

The recursion method, which solves coupled Heisenberg equations in a Lanczos operator basis, has recently emerged as a powerful nonperturbative tool for computing dynamical correlation functions in strongly correlated two- and…

It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…

It is known that Einstein's conceptual base for his theory of relativity was the philosophy formulated by Immanuel Kant. Things appear differently to observers in different frames. However, Kant's Ding-an-Sich leads to the existence of the…

In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat…

The objective of this series of three papers is to axiomatically derive quantum mechanics from classical mechanics and two other basic axioms. In this first paper, Schreodinger's equation for the density matrix is fist obtained and from it…

We try to clarify what are the genuine quantal effects that are associated with generalized Brownian Motion (BM). All the quantal effects that are associated with the Zwanzig-Feynman-Vernon-Caldeira-Leggett model are (formally) a solution…