Evaluation of cross section of elastic scattering for non-relativistic and relativistic particles by means of fundamental scattering formulas

Wang, Huaiyu

doi:10.12988/astp.2022.91866

Cited by 5 publications

(5 citation statements)

References 14 publications

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“…We will enter QED. In a previous work [54], the Green's functions were given, and the cross sections were evaluated up to the first-order term. In later works, we will revisit the topics in QED by means of the generalized scattering formulas presented in this paper, and clarify the role of the negative kinetic energy (NKE) solutions of relativistic quantum mechanics equations.…”

Section: Discussionmentioning

confidence: 99%

A generalized scattering theory in quantum mechanics

Wang

2023

J. Phys. Commun.

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In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of particle. In laboratory frame, a generalized Lippmann-Schwinger scattering equation is derived. We emphasized that the derivation is rigorous, even for treating infinitesimals. No manual operation such as analytical continuation is allowed. In the case that before scattering N particles are plane waves and after the scattering they are new plane waves, the transition amplitude and transition probability are given and the generalized S matrix is presented. It is proved that the transition probability from a set of plane waves to a new set of plane waves of the N particles equal to that of the reciprocal process. The generalized theory is applied to the cases of one- and two-particle scattering as two examples. When applied to single-particle scattering problems, our generalized formalism degrades to that usually seen in the literature. When our generalized theory is applied to two-particle scattering problems, the formula of the transition probability of two-particle collision is given. It is shown that the transition probability of the scattering of two free particles is identical to that of the reciprocal process. This transition probability and the identity are needed in deriving Boltzmann transport equation in statistical mechanics. The case of identical particles is also discussed.

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Section: Discussionmentioning

confidence: 99%

A generalized scattering theory in quantum mechanics

Wang

2023

J. Phys. Commun.

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“…(3.16) is respectively modified to be . We [54] utilized these formulas to evaluate the differential cross sections up to the first order for both the low-momentum and relativistic particles in three-, two-, and one-dimensional spaces.…”

Section: Singe-particle Scatteringmentioning

confidence: 99%

A Generalized Scattering Theory in Quantum Mechanics

Wang

2023

Preprint

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“…The content of physics research has been matter with PKE. We [1][2][3][4][5][6][7][8][9][10][11][12] conducted a series of studies on the NKE substances. All the physical laws we have known remain unchanged, such as thermodynamics, statistical mechanics, classical mechanics, quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

A Physical Mechanism of the Generation of Stable Positive Kinetic Energy Systems and a Qualitative Explanation of the Proportions of the Four Ingredients in the Universe

Wang¹

2023

Preprint

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The author’s opinion is that the negative energy solutions of the Dirac equation mean that a particle can be of negative kinetic energy (NKE) besides positive kinetic energy (PKE). We think that NKE particles are dark ones and NKE matter is dark matter. In our previous works, the dark matter theory of the NKE version and the dark energy theory that matched dark matter theory were put forth. In this work, we investigate the topics related to the metamorphosis of objects between PKE and NKE. We first evaluate the collosions between a PKE and a NKE particles. A scenario of accelerating PKE particles is raised. We put forth the cosmic dark radiation background and gravity potential background. In the universe, negative energy is predominating. In the observable universe, substances constitute stable PKE systems. The total energy of every such system is negative. We propose a mechanism that NKE substances combine into stable PKE systems. Macroscopically, NKE objects can constitute stable PKE astrophysical systems by means of gravity between them. Microscopically, NKE particles can combine into stable PKE systems by means of attractive interactions between them, say, Coulomb attraction. Currently, people think that there are four ingrediants in the universe: photons \Omega_R0, matter \Omega_M0, dark matter \Omega_DM, and dark energy \Omega_\lambda0. We analyze the order of the appearance of the four ingredients and conclude that qualitatively, their proportions should be \Omega_\lambda0 > \Omega_DM > \Omega_M0 > \Omega_R0.

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Evaluation of cross section of elastic scattering for non-relativistic and relativistic particles by means of fundamental scattering formulas

Cited by 5 publications

References 14 publications

A generalized scattering theory in quantum mechanics

A generalized scattering theory in quantum mechanics

A Generalized Scattering Theory in Quantum Mechanics

A Physical Mechanism of the Generation of Stable Positive Kinetic Energy Systems and a Qualitative Explanation of the Proportions of the Four Ingredients in the Universe

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