Exploring the propagation of relativistic quantum wavepackets in the trajectory-based formulation

Hung-Ming Tsai; Bill Poirier

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Exploring the propagation of relativistic quantum wavepackets in the trajectory-based formulation

机译：在基于轨迹的公式中探索相对论量子波包的传播

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Inthecontextofnonrelativisticquantummechanics,Gaussianwavepacketsolutionsofthetime-dependentSchr?dingerequationprovideusefulphysicalinsight.Thisisnotthecaseforrelativisticquantummechanics,however,forwhichboththeKlein-GordonandDiracwaveequationsresultinstrangeandcounterintuitivewavepacketbehaviors,evenforfree-particleGaussians.Thesebehaviorsincludezitterbewegungandotherinterferenceeffects.Asapotentialremedy,thispaperexploresanewtrajectory-basedformulationofquantummechanics,inwhichthewavefunctionplaysnorole[Phys.Rev.X,4,040002(2014)].Quantumstatesarerepresentedasensemblesoftrajectories,whosemutualinteractionisthesourceofallquantumeffectsobservedinnature—suggestinga"manyinteractingworlds"interpretation.Itisshownthattherelativisticgeneralizationofthetrajectory-basedformulationresultsinwell-behavedfree-particleGaussianwavepacketsolutions.Inparticular,probabilitydensityispositiveandwell-localizedeverywhere,anditsspatialintegralisconservedovertime—inanyinertialframe.Finally,theensemble-averagedwavepacketmotionisalongastraightlinepaththroughspacetime.Inthismanner,thepathologiesofthewave-basedrelativisticquantumtheory,asappliedtowavepacketpropagation,areavoided...

机译：Inthecontextofnonrelativisticquantummechanics，Gaussianwavepacketsolutionsofthetime-dependentSchr？dingerequationprovideusefulphysicalinsight.Thisisnotthecaseforrelativisticquantummechanics然而，forwhichboththeKlein-GordonandDiracwaveequationsresultinstrangeandcounterintuitivewavepacketbehaviors，evenforfree-particleGaussians.Thesebehaviorsincludezitterbewegungandotherinterferenceeffects.Asapotentialremedy，thispaperexploresanewtrajectory-basedformulationofquantummechanics，inwhichthewavefunctionplaysnorole [Phys.Rev.X，4,040002（2014）]。Quantumstatesarerepresentedasensemblesoftrajectories，whosemutualinteractionisthesourceofallquantumeffectsobservedinnature-suggestinga”它表明，基于轨迹的公式的热力学一般化结果表现为行为良好的自由粒子高斯波包解决方案。特别是，概率密度为正值且均位于局部，并且其空间积分在任何不大的帧内都可以长期保持。 edwavepacket运动沿时空沿直线延伸。在这种方式下，避免了基于波的相对论量子论的病理学应用于波包传播。

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《Journal of Physics: Conference Series》 |2016年第1期|共页
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Hung-Ming Tsai; Bill Poirier;
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Exploring the propagation of relativistic quantum wavepackets in the trajectory-based formulation

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