Related papers: Understanding the Schrodinger equation as a kinema…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
Since its emergence, quantum mechanics has been a challenge for an understanding of reality which is based on our intuition in a classical world. Nevertheless, it has often been tried to impose this understanding of reality on quantum…
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…
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…
The momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In…
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…
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…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
In learning quantum mechanics, an essential question has always been: How does one go about developing a "physical feel" for quantum phenomena? Naturally, one needs a basis or ground zero to start from, and that basis must be unlike…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
In physics, one is often misled in thinking that the mathematical model of a system is part of or is that system itself. Think of expressions commonly used in physics like "point" particle, motion "on the line", "smooth" observables, wave…
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…
We present a new formulation for the emergence of classical dynamics in a quantum world by considering a path integral approach that also incorporates continuous measurements. Our program is conceptually different from the decoherence…
The measurement problem in quantum mechanics originates in the inability of the Schr\"odinger equation to predict definite outcomes of measurements. This is due to the lack of objectivity of the eigenstates of the measuring apparatus. Such…
A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger's algebra of selective measurements and helps to understand its scope and eventual…
An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
Schroedinger's first proposal for the interpretation of quantum mechanics was based on a postulate relating the wave function on configuration space to charge density in physical space. Schroedinger apparently later thought that his…
This work develops a conceptual framework for the foundations of quantum physics, linking two main approaches: the algebraic formulation and quantum probability. Rather than proposing new axioms or theories, the text reorganizes and…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…