Related papers: The third way to quantum mechanics is the forgotte…
The procedure used to "do physics" in the macroscopic world is familiar: You take an object, start it off with a particular position and velocity, subject it to known forces (say gravity or friction, or both), and follow its trajectory. You…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
The formalism of quantum mechanics produces spectacular results, but its rules, its parameters are empirical, either deduced from classical physics, or from experimental results rather than from the postulates. Thus, quantum mechanics is…
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…
In July 1925 Heisenberg published a paper [Z. Phys. 33, 879-893 (1925)] which ended the period of `the Old Quantum Theory' and ushered in the new era of Quantum Mechanics. This epoch-making paper is generally regarded as being difficult to…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
To understand the foundations of quantum mechanics, we have to think carefully about how theoretical concepts are rooted in -- and limited by -- the nature of experience, as Bohr attempted to show. Geometrical pictures of physical phenomena…
In 1926, Erwin Schrodinger wrote a series of papers that invented wave mechanics and set the foundation for much of the single-particle quantum mechanics that we teach today. In his first paper, he solved the Schrodinger equation using the…
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…
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…
An introduction to some basic ideas of the author's "quantum cybernetics" is given, which depicts waves and "particles" as mutually dependent system components, thus defining "organizationally closed systems" characterized by a fundamental…
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…
We are interested here in the program of reconstruction of quantum mechanics of the German physicist and philosopher Carl Friedrich von Weizs\"{a}cker, which still has some supporters today. In the major part of this article, we limit…
Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in the Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism…
After the development of a self-consistent quantum formalism nearly a century ago there began a quest for how to interpret the theoretical constructs of the formalism. In fact, the pursuit of new interpretations of quantum mechanics…
We begin by discussing ``What exists?'', i.e. ontology, in Classical Physics which provided a description of physical phenomena at the macroscopic level. The microworld however necessitates a introduction of Quantum ideas for its…
Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear…
For the simple system of a point-like particle confined to a straight line, I compile, initially in a concise table, the structural elements of quantum mechanics and contrast them with those of classical (statistical) mechanics. Despite…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the…