On the Cutting of a Particle Wave

Abstract For multi-time wave functions, which naturally arise as the relativistic particle-position representation of the quantum state vector, the analog of the Schrödinger equation consists of several equations, one for each time variable. This leads to the question of how to prove the consistency of such a system of PDEs. The question becomes more difficult for theories with particle creation, as then different sectors of the wave function have different numbers of time variables. Petrat and Tumulka (2014) gave an example of such a model and a non-rigorous argument for its consistency. We give here a rigorous version of the argument after introducing an ultraviolet cut-off into the creation and annihilation terms of the multi-time evolution equations. These equations form an infinite system of coupled PDEs; they are based on the Dirac equation but are not fully relativistic (in part because of the cut-off). We prove the existence and uniqueness of a smooth solution to this system for every initial wave function from a certain class that corresponds to a dense subspace in the appropriate Hilbert space.Abstract For multi-time wave functions, which naturally arise as the relativistic particle-position representation of the quantum state vector, the analog of the Schrödinger equation consists of several equations, one for each time variable. This leads to the question of how to prove the consistency of such a system of PDEs. The question becomes more difficult for theories with particle creation, as then different sectors of the wave function have different numbers of time variables. Petrat and Tumulka (2014) gave an example of such a model and a non-rigorous argument for its consistency. We give here a rigorous version of the argument after introducing an ultraviolet cut-off into the creation and annihilation terms of the multi-time evolution equations. These equations form an infinite system of coupled PDEs; they are based on the Dirac equation but are not fully relativistic (in part because of the cut-off). We prove the existence and uniqueness of a smooth solution to this system for every initial wave function from a certain class that corresponds to a dense subspace in the appropriate Hilbert space.

arXiv:2001.05920Annales Henri PoincaréApr 1, 20217 citations

Discuss wave-particle duality of light

BI Si-wen

In the study of quantum remote sensing, quantum spectral imaging. Since the beginning of 2001, after three stages of basic theory, scientific experiment and key technology research, has made breakthrough progress and innovative results. With the deepening of the research work and needs, some basic theoretical issues and cutting-edge technical problems need to be explored and studied. This paper discusses wave-particle duality of light is one of the important content. In more than and 100 years, wave-particle duality of light as research has made important progress. But the wave-particle duality of light is like what? Wave-particle duality of light like mechanism is what? Has been the most intense debate on the issue of Optics and physicists. In this paper, the author firstly summarizes the wave-particle duality of light development history and present situation of the research study, describes the research ideas of wave-particle duality of light; on this basis, the author puts forward the application of lightstring concept focuses on the wave-particle duality of light phenomenological characteristic geometry shape and movement of the content; describes the wave-particle duality of light like generated string-light effect mechanism. To study the wave-particle duality of light like two, a profound understanding of wave-particle duality of light nature, put forward a new research method.In the study of quantum remote sensing, quantum spectral imaging. Since the beginning of 2001, after three stages of basic theory, scientific experiment and key technology research, has made breakthrough progress and innovative results. With the deepening of the research work and needs, some basic theoretical issues and cutting-edge technical problems need to be explored and studied. This paper discusses wave-particle duality of light is one of the important content. In more than and 100 years, wave-particle duality of light as research has made important progress. But the wave-particle duality of light is like what? Wave-particle duality of light like mechanism is what? Has been the most intense debate on the issue of Optics and physicists. In this paper, the author firstly summarizes the wave-particle duality of light development history and present situation of the research study, describes the research ideas of wave-particle duality of light; on this basis, the author puts forward the application of lightstring concept focuses on the wave-particle duality of light phenomenological characteristic geometry shape and movement of the content; describes the wave-particle duality of light like generated string-light effect mechanism. To study the wave-particle duality of light like two, a profound understanding of wave-particle duality of light nature, put forward a new research method.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEFeb 28, 20179 citations

Particles as Waves

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato

Springer eBooksJan 1, 19990 citations

Planar three-body bound states induced by $p$ -wave interatomic resonancePlanar three-body bound states induced by $p$-wave interatomic resonance

Maxim A. Efremov, Wolfgang P. Schleich

We consider the bound states of a system consisting of a light particle and two heavy bosonic ones, which are restricted in their quantum mechanical motion to two space dimensions. A $p$ -wave resonance in the heavy-light short-range potential establishes the interaction between the two heavy particles. Due to the large ratio of the atomic masses this planar three-body system is perfectly suited for the Born-Oppenheimer approximation which predicts a Coulomb energy spectrum with a Gaussian cut-off.We consider the bound states of a system consisting of a light particle and two heavy bosonic ones, which are restricted in their quantum mechanical motion to two space dimensions. A $p$-wave resonance in the heavy-light short-range potential establishes the interaction between the two heavy particles. Due to the large ratio of the atomic masses this planar three-body system is perfectly suited for the Born-Oppenheimer approximation which predicts a Coulomb energy spectrum with a Gaussian cut-off.

arXiv:1511.07815Nov 24, 20151 citation

Particles as Waves

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato +2 more

Springer eBooksJan 1, 20090 citations

Planar three-body bound states induced by

p

-wave interatomic resonance

We consider the bound states of a system consisting of a light particle and two heavy bosonic ones, which are restricted in their quantum mechanical motion to two space dimensions. A

p

-wave resonance in the heavy-light short-range potential establishes the interaction between the two heavy particles. Due to the large ratio of the atomic masses this planar three-body system is perfectly suited for the Born-Oppenheimer approximation which predicts a Coulomb energy spectrum with a Gaussian cut-off.