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On The Quantum Mechanics for One Photon

Ya-Peng Hu, Weigang Qiu, Hongbao Zhang

Published Jan 1, 2008• 2 citations
OpenAlex

Abstract

This paper revisits the quantum mechanics for one photon from the modern viewpoint and by the geometrical method. Especially, besides the ordinary (rectangular) momentum representation, for the first time we provide the other two important representations, called the cylindrically symmetrical representation and the spherically symmetrical representation respectively. These other two representations are relevant to some of current photon experiments in quantum optics. In addition, the latter is useful for us to extract the information on the quantized black holes. The framework and approach presented here are also applicable to other particles with arbitrary mass and spin, such as the particle with spin 1 2. 1

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On the quantum mechanics for one photon

Yapeng Hu, Weigang Qiu, Hongbao Zhang

This paper revisits the quantum mechanics for one photon from the modern viewpoint and by the geometrical method. Especially, besides the ordinary (rectangular) momentum representation, we provide an explicit derivation for the other two important representations, called the cylindrically symmetrical representation and the spherically symmetrical representation, respectively. These other two representations are relevant to some current photon experiments in quantum optics. In addition, the latter is useful for us to extract the information on the quantized black holes. The framework and approach presented here are also applicable to other particles with arbitrary mass and spin, such as the particle with spin 12.

arXiv:quant-ph/0509216•Journal of Mathematical Physics•May 1, 2006•2 citations

On the First Quantization Theory of Photon

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Abstract:Geometrical optics has high similarity with classical particle mechanics. After first quantization program classical particle mechanics can obtain non-relativistic quantum mechanics that suitable for micro, but quantum mechanics does not describe the photon that its static mass is zero. So whether there is a kind of "quantization " approach for geometrical optics, by which non-relativistic quantum mechanics that can be used to describe the photon can be obtained. It’s quantum mechanics of photon similar to the Schrödinger wave mechanics under the neglection of the formation and annihilation of photon. In this paper, several methods that can be used to find

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Quantum-mechanical Explanation of Young’s double Slit Experiment through Simulation of the Photon Coordinate Wave Function

Alexandr Petrovich Davydov, Tatiana Pavlovna Zlydneva

Introduction: In the rapidly developing areas of photonics associated with quantum teleportation of photons, quantum cryptography, and quantum computing, ideas are becoming increasingly relevant about the certain localized states of single or several entangled photons moving in space and time. As is known, in quantum mechanics, localized states of particles can only be described using wave functions in coordinate representation – the corresponding wave packets. Aims: To explain Young's one- and two-photon experiments using coordinate 6-component quantum mechanical and 1-component quasi-classical photon wave functions. Methods: The article outlines the method developed in authors' previous work in constructing the 6-component coordinate wave function of free photons in the form of the wave packet (an integral over the entire momentum space and sum over two possible values +1 and -1 of the helicity). The basis functions are the circularly polarized monochromatic waves, corresponding to certain values of the momentum, helicity, and photon energy operators and forming a complete orthonormal set of generalized eigenfunctions of these operators. This photon wave function (PWF) is normalized to the unit probability of finding the photon anywhere in space. Both the basis functions and the coordinate PWF satisfy a Schrödinger-type equation derived from the Maxwell-Lorentz equations written in quantum mechanical form first introduced by Majorana. Then the results of modeling and consideration of the space-time evolution of the wave packet with Gaussian momentum distribution corresponding to the directed photon emission for 80 fs are briefly presented. Further, in view of the possibility of constructing the coordinate PWF, the basic formula for the waveparticle duality of photons and particles is formulated. It is emphasized that the photon is fundamentally different from “ordinary” particles, since, according to the authors, the photon is the result of the propagation of a certain complex spin wave in a physical vacuum, the details of which can only be considered simultaneously with the study of the structure of the physical vacuum at Planckian distances. Results: Young`s one- and two-photon experiments are explained using various options for modeling 6-component coordinate PWFs, including approximate functions corresponding to spherically symmetric and electric dipole photon radiation. Conclusion: This explanation is illustrated using specific examples of radiation and, at the same time, is compared with numerical simulations for spherically symmetric radiation and the use of 1-component quasi-classical PWFs.

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Photon-based and classical descriptions in nanophotonics: a review

Davıd L. Andrews

The centrality of the photon concept in modern physics is strongly evident in wide spheres of photonics and nanophotonics. Despite the resilience and persistence of earlier classical representations, there are numerous optical features and phenomena that only truly photon-based descriptions of theory can properly address. It is crucial to cast theory in terms of observables, and in this respect the quantum theory of light engages most directly and pragmatically with experiment. No other theory adequately reconciles the discreteness in energy of optical quanta, with their characteristic quantum mechanical delocalization in space. Examples of the distinctiveness of a photonic representation are to be found in nonclassical optical correlations; intensity fluctuations and phase; polarization, spin, and information content; measures of optical chirality; near-field interactions; and plasmonics. Increasingly, links between these fundamental properties and features are proving significant in the context of nanoscale interactions. Yet, even as new technologies are being built on the framework of modern photonics, a number of difficult questions surrounding the nature of the photon still remain. Both in its flourishing applications and in matters of fundamental entity, the photon is still a subject very much at the heart of current research.

Journal of Nanophotonics•Mar 17, 2014•12 citations

The Photon as a Particle: The General One-Photon State

E R Pike frs, Sarben Sarkar

Abstract Through the classic work of Planck, Einstein, and others the particle nature of the photon has been established. In the previous chapter we considered the wave field of the photon. In this chapter we will emphasize more its particle nature and discuss the extent to which a wave function with a probabilistic interpretation is an appropriate description. Once we have the concept of a particle it is natural to ask how localized the state can be. The degree of localizability of photons is of concern in the interpretation of experiments in quantum optics involving weak light sources and non-linear electromagnetic media. If a photon is not to have the structure of a composite particle its quantum states should be describable by translations, rotations, and Lorentz boosts of a particular state and possibly super positions of such states. This is equivalent to a photon being associated with an irreducible representation of the Poincaré group. A brief overview of the general theory of group representations is given in Appendix 3. We will be able to give a complete discussion of the representations of the Poincaré group pertinent to the photon. Our discussion of localizability will be quite rigorous but we will gloss over measure-theoretic niceties. For more mathematical discussions the reader can refer to the works of Mackey (1978) and Wightman (1962). We will finish the chapter by examining the implication of Poincaré invariance for the metric on the space of quantum states of the photon.

•Dec 7, 1995•0 citations

The de Broglie-Bohm Interpretation of Evaporating Black-Holes

J. Acácio de Barros, G. Oliveira-Neto, Vale, T. B.

In this work we apply the de Broglie-Bohm interpretation of quantum mechanics to the quantized spherically symmetric black-hole coupled to a massless scalar field. The wave-functional used was first obtained by Tomimatsu using the standard ADM quantization and a gauge that places the observer close to the black-hole horizon. Using the causal interpretation, we compute quantum trajectories determined by the initial conditions. We show that the quantum trajectories for the black-hole mass can either increase or decrease with time. The quantum trajectories that show increasing mass represent the usual black-hole behavior of continuous energy absorption. The mass-decreasing quantum trajectories are a purely quantum mechanical phenomena. They can be physically interpreted as describing a black-hole that evaporates.

arXiv:gr-qc/0404073•Apr 16, 2004•0 citations
This paper revisits the quantum mechanics for one photon from the modern viewpoint and by the geometrical method. Especially, besides the ordinary (rectangular) momentum representation, for the first time we provide the other two important representations, called the cylindrically symmetrical representation and the spherically symmetrical representation respectively. These other two representations are relevant to some of current photon experiments in quantum optics. In addition, the latter is useful for us to extract the information on the quantized black holes. The framework and approach presented here are also applicable to other particles with arbitrary mass and spin, such as the particle with spin 1 2. 1
This paper revisits the quantum mechanics for one photon from the modern viewpoint and by the geometrical method. Especially, besides the ordinary (rectangular) momentum representation, we provide an explicit derivation for the other two important representations, called the cylindrically symmetrical representation and the spherically symmetrical representation, respectively. These other two representations are relevant to some current photon experiments in quantum optics. In addition, the latter is useful for us to extract the information on the quantized black holes. The framework and approach presented here are also applicable to other particles with arbitrary mass and spin, such as the particle with spin 12.
Abstract:Geometrical optics has high similarity with classical particle mechanics. After first quantization program classical particle mechanics can obtain non-relativistic quantum mechanics that suitable for micro, but quantum mechanics does not describe the photon that its static mass is zero. So whether there is a kind of "quantization " approach for geometrical optics, by which non-relativistic quantum mechanics that can be used to describe the photon can be obtained. It’s quantum mechanics of photon similar to the Schrödinger wave mechanics under the neglection of the formation and annihilation of photon. In this paper, several methods that can be used to find
Introduction: In the rapidly developing areas of photonics associated with quantum teleportation of photons, quantum cryptography, and quantum computing, ideas are becoming increasingly relevant about the certain localized states of single or several entangled photons moving in space and time. As is known, in quantum mechanics, localized states of particles can only be described using wave functions in coordinate representation – the corresponding wave packets. Aims: To explain Young's one- and two-photon experiments using coordinate 6-component quantum mechanical and 1-component quasi-classical photon wave functions. Methods: The article outlines the method developed in authors' previous work in constructing the 6-component coordinate wave function of free photons in the form of the wave packet (an integral over the entire momentum space and sum over two possible values +1 and -1 of the helicity). The basis functions are the circularly polarized monochromatic waves, corresponding to certain values of the momentum, helicity, and photon energy operators and forming a complete orthonormal set of generalized eigenfunctions of these operators. This photon wave function (PWF) is normalized to the unit probability of finding the photon anywhere in space. Both the basis functions and the coordinate PWF satisfy a Schrödinger-type equation derived from the Maxwell-Lorentz equations written in quantum mechanical form first introduced by Majorana. Then the results of modeling and consideration of the space-time evolution of the wave packet with Gaussian momentum distribution corresponding to the directed photon emission for 80 fs are briefly presented. Further, in view of the possibility of constructing the coordinate PWF, the basic formula for the waveparticle duality of photons and particles is formulated. It is emphasized that the photon is fundamentally different from “ordinary” particles, since, according to the authors, the photon is the result of the propagation of a certain complex spin wave in a physical vacuum, the details of which can only be considered simultaneously with the study of the structure of the physical vacuum at Planckian distances. Results: Young`s one- and two-photon experiments are explained using various options for modeling 6-component coordinate PWFs, including approximate functions corresponding to spherically symmetric and electric dipole photon radiation. Conclusion: This explanation is illustrated using specific examples of radiation and, at the same time, is compared with numerical simulations for spherically symmetric radiation and the use of 1-component quasi-classical PWFs.
The centrality of the photon concept in modern physics is strongly evident in wide spheres of photonics and nanophotonics. Despite the resilience and persistence of earlier classical representations, there are numerous optical features and phenomena that only truly photon-based descriptions of theory can properly address. It is crucial to cast theory in terms of observables, and in this respect the quantum theory of light engages most directly and pragmatically with experiment. No other theory adequately reconciles the discreteness in energy of optical quanta, with their characteristic quantum mechanical delocalization in space. Examples of the distinctiveness of a photonic representation are to be found in nonclassical optical correlations; intensity fluctuations and phase; polarization, spin, and information content; measures of optical chirality; near-field interactions; and plasmonics. Increasingly, links between these fundamental properties and features are proving significant in the context of nanoscale interactions. Yet, even as new technologies are being built on the framework of modern photonics, a number of difficult questions surrounding the nature of the photon still remain. Both in its flourishing applications and in matters of fundamental entity, the photon is still a subject very much at the heart of current research.
Abstract Through the classic work of Planck, Einstein, and others the particle nature of the photon has been established. In the previous chapter we considered the wave field of the photon. In this chapter we will emphasize more its particle nature and discuss the extent to which a wave function with a probabilistic interpretation is an appropriate description. Once we have the concept of a particle it is natural to ask how localized the state can be. The degree of localizability of photons is of concern in the interpretation of experiments in quantum optics involving weak light sources and non-linear electromagnetic media. If a photon is not to have the structure of a composite particle its quantum states should be describable by translations, rotations, and Lorentz boosts of a particular state and possibly super positions of such states. This is equivalent to a photon being associated with an irreducible representation of the Poincaré group. A brief overview of the general theory of group representations is given in Appendix 3. We will be able to give a complete discussion of the representations of the Poincaré group pertinent to the photon. Our discussion of localizability will be quite rigorous but we will gloss over measure-theoretic niceties. For more mathematical discussions the reader can refer to the works of Mackey (1978) and Wightman (1962). We will finish the chapter by examining the implication of Poincaré invariance for the metric on the space of quantum states of the photon.
In this work we apply the de Broglie-Bohm interpretation of quantum mechanics to the quantized spherically symmetric black-hole coupled to a massless scalar field. The wave-functional used was first obtained by Tomimatsu using the standard ADM quantization and a gauge that places the observer close to the black-hole horizon. Using the causal interpretation, we compute quantum trajectories determined by the initial conditions. We show that the quantum trajectories for the black-hole mass can either increase or decrease with time. The quantum trajectories that show increasing mass represent the usual black-hole behavior of continuous energy absorption. The mass-decreasing quantum trajectories are a purely quantum mechanical phenomena. They can be physically interpreted as describing a black-hole that evaporates.