Quantum theory of photons based on the first quantization technique,similar to that used by Schrödinger in the formulation of quantum mechanics,is considered.First,scalar quantum mechanics of photons operating wi...Quantum theory of photons based on the first quantization technique,similar to that used by Schrödinger in the formulation of quantum mechanics,is considered.First,scalar quantum mechanics of photons operating with the photon wave functions is discussed.Using the first quantization,the wave equation,the Schrödinger-like equations,and the Dirac equation for photons are derived.Then,vector quantum mechanics of photons is introduced,which defines the electromagnetic vector fields.Using the first quantization,the Maxwell equations for photons in a magneto-dielectric medium are obtained.Because the photon’s electric and magnetic fields satisfy the Maxwell equations,all that is known about the classical optical fields can be directly transferred to photons demonstrating their quantum diversity.Relationships between the scalar and vector quantum mechanics of photons and between the Dirac and Maxwell equations are analyzed.To describe the propagation of photons in dispersive media,modified Maxwell equations are introduced.展开更多
基金support from the DFG,German Research Foundation under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD(EXC 2122,Project ID 390833453)the Cluster of Excellence QuantumFrontiers(EXC 2123,Project ID 390837967).I thank Dr.A.Evlyukhin for critical discussions.
文摘Quantum theory of photons based on the first quantization technique,similar to that used by Schrödinger in the formulation of quantum mechanics,is considered.First,scalar quantum mechanics of photons operating with the photon wave functions is discussed.Using the first quantization,the wave equation,the Schrödinger-like equations,and the Dirac equation for photons are derived.Then,vector quantum mechanics of photons is introduced,which defines the electromagnetic vector fields.Using the first quantization,the Maxwell equations for photons in a magneto-dielectric medium are obtained.Because the photon’s electric and magnetic fields satisfy the Maxwell equations,all that is known about the classical optical fields can be directly transferred to photons demonstrating their quantum diversity.Relationships between the scalar and vector quantum mechanics of photons and between the Dirac and Maxwell equations are analyzed.To describe the propagation of photons in dispersive media,modified Maxwell equations are introduced.
