New results by low momentum approximation from relativistic quantum mechanics equations and suggestion of experiments

Wang, Huaiyu

doi:10.1088/2399-6528/abd00b

Cited by 10 publications

(35 citation statements)

References 87 publications

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“…There are NKE solutions in (A.1), but not in (A.2). In fact, we have shown [1] that the transformation ( )…”

Section: Appendix the Negative Energy Solutions Of Dirac Equation Are Not Antiparticlesmentioning

confidence: 97%

“…If the transitions result in releasing energies, we may observe some, but it seems not so. This problem is left to being dealt with later, which was also mentioned in the end of appendix D of the author's previous paper [1].…”

Section: Clausius Statementmentioning

confidence: 99%

“…The former two belong to positive energy ( ) + E and the latter two to negative energy ( ) -E . The expressions of the solutions are equations (A.16)-(A.19) in our previous paper [1]. Let us inspect, for instance, the solution ( ) y +  .…”

Section: Appendix the Negative Energy Solutions Of Dirac Equation Are Not Antiparticlesmentioning

confidence: 99%

“…E E E . A free particle is a simplest case of V=0, and two examples were given [1]. One was an infinitely high potential barrier, and another was a Coulomb repulsive potential.…”

Section:  -= + + -mentioning

confidence: 99%

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Fundamental formalism of statistical mechanics and thermodynamics of negative kinetic energy systems

Wang¹

2021

J. Phys. Commun.

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The solutions of a particle's Dirac equation contains a negative kinetic energy (NKE) branch. Such an energy spectrum has an upper limit but no lower limit, so that the system with this spectrum, called NKE system, is of negative temperature. Fundamental formulas of statistical mechanics and thermodynamics of NKE systems are presented. All the formulas have the same forms of those of positive kinetic energy (PKE) systems. Almost all thermodynamic quantities, except entropy and specific heat, have a contrary sign compared to those of PKE systems. Specially, pressure is negative and its microscopic mechanism is given. Entropy is always positive and Boltzmann entropy formula remains valid. The three laws of thermodynamics remain valid, as long as the thermodynamic quantities have a negative sign. Negative temperature Carnot engine can work between two negative temperatures. Since the NKE levels need not be fully filled, it is argued that the concept of Dirac's Fermion Sea can be totally abandoned.

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“…There are NKE solutions in (A.1), but not in (A.2). In fact, we have shown [1] that the transformation ( )…”

Section: Appendix the Negative Energy Solutions Of Dirac Equation Are Not Antiparticlesmentioning

confidence: 97%

Section: Clausius Statementmentioning

confidence: 99%

Section: Appendix the Negative Energy Solutions Of Dirac Equation Are Not Antiparticlesmentioning

confidence: 99%

“…E E E . A free particle is a simplest case of V=0, and two examples were given [1]. One was an infinitely high potential barrier, and another was a Coulomb repulsive potential.…”

Section:  -= + + -mentioning

confidence: 99%

See 2 more Smart Citations

Fundamental formalism of statistical mechanics and thermodynamics of negative kinetic energy systems

Wang¹

2021

J. Phys. Commun.

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“…In a previous work [10], we were aware of the inconsistency between Schrödinger equation and the low momentum approximations of RQMEs, and suggested the way how to remedy the inconsistency. The main result was that a relativistic particle had solutions of negative energy branch which meant that a particle could have negative kinetic energy (NKE) besides positive kinetic energy (PKE).…”

Section: Introductionmentioning

confidence: 99%

The Modified Fundamental Equations of Quantum Mechanics in Symmetric Forms

Wang¹

2021

Preprint

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Up to now, Schrödinger equation, Klein-Gordon equation (KGE) and Dirac equation are believed the fundamental equations of quantum mechanics. Schrödinger equation has a defect that there is no NKE solutions. Dirac equation has positive kinetic energy (PKE) and negative kinetic energy (NKE) branches. Both branches should have low momentum, or nonrelativistic, approximations: one is Schrödinger equation and the other is NKE Schrödinger equation. KGE has two problems: it is an equation of second time derivative, and calculated density is not definitely positive. To overcome the problems, it should be revised as PKE and NKE decoupled KGEs. The fundamental equations of quantum mechanics after the modification have at least two merits. They are of unitary in that everyone contains the first time derivative and are symmetric with respect to PKE and NKE. This reflects the symmetry of the PKE and NKE matters, as well as matter and dark matter, of our universe. The problems of one-dimensional step potentials are resolved by means of the modified fundamental equations for a nonrelativistic particle.

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Solving Klein’s paradox

Wang

2020

J. Phys. Commun.

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We figure out the famous Klein’s paradox arising from the reflection problem when a Dirac particle encounters a step potential with infinite width. The key is to piecewise solve Dirac equation in such a way that in the region where the particle’s energy E is greater (less) than the potential V, the solution of the positive (negative) energy branch is adopted. In the case of Klein–Gordon equation with a piecewise constant potential, the equation is decoupled to positive and negative energy equations, and reflection problem is solved in the same way. Both infinitely and finitely wide potentials are considered. The reflection coefficient never exceeds 1. The results are applied to discuss the transmissions of particles with no mass or with very small mass.

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New results by low momentum approximation from relativistic quantum mechanics equations and suggestion of experiments

Abstract: New results by low momentum approximation from relativistic quantum mechanics equations and suggestion of experimentsTo cite this article: Huai-Yu Wang 2020 J. Phys. Commun. 4 125004 View the article online for updates and enhancements.

Cited by 10 publications

References 87 publications

Fundamental formalism of statistical mechanics and thermodynamics of negative kinetic energy systems

Fundamental formalism of statistical mechanics and thermodynamics of negative kinetic energy systems

The Modified Fundamental Equations of Quantum Mechanics in Symmetric Forms

Solving Klein’s paradox

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