ATTEMPT AT FORMULATING THE CONSERVATIONS OF ENERGY AND MOMENTUM IN COMPTON SCATTERING WITH QUANTUM MECHANICAL CONCEPTS
Bohr et al.once believed that both the conservation of energy and the conservation of momentum in a microscopic process are statistically conserved.And then Bothe et al.veri-fied that the laws of the conservations of total energy and total momentum of an electron and an X-ray photon before and after a single collision are strictly valid by using the Compton scat-tering experiment,and such results also denied statistical conservation.There are expressions about strict conservations of total energy and total momentum of the system in Compton scat-tering experiment without quantum mechanical concepts in the introductions of some quantum mechanics books.Different from this,the aim of this paper is attempt to express those with quantum mechanical concepts.There is no expression about the strict conservation and the statistical conservation of physical quantities in quantum mechanics books.Our viewpoints are that the total energy and the total momentum of an isolated system are strict conservation by exchanging energy and momentum within the system in the evolution of the system state,and the momentum and kinetic energy(an interaction energy is not all belong to anyone subsys-tem)of a subsystem are statistical conservation.The"strict conservation"in journal articles is different from ours.A recent paper by the corresponding author of this paper and his coau-thors(Int.J Theor.Phys.,2020,59:229)used the terms of strict conservation and statistical conservation(we offer more precise statements in this paper,and these statements have some differences with that of a conserved physical quantity),and offered the expression ways of the strict conservation of total momentum for an isolated composite system and the statistical con-servation of momentum for a subsystem in terms of the concepts of entangled states and ei-genvalues.In this paper,we try to use these concepts and mixed states to express the strict conservations of total energy and total momentum of the system before and after a Compton scattering,and also explain the statistical conservations of energy(no interaction after scatter-ing)and momentum of a subsystem.Similarly,we can express the strict conservations of some physical quantities of an isolated composite system and the statistical conservations of some physical quantities of a subsystem with quantum mechanical concepts.
Compton scatteringstrict conservationstatistical conservationentangled statemixed state
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