Schrfdinger＇s equation is one the equations that mark the beginnings of the systematic quantum physics. It was shown that it follows from the Dirac＇s equation and the relationship with classical physics, i.e. with c...Schrfdinger＇s equation is one the equations that mark the beginnings of the systematic quantum physics. It was shown that it follows from the Dirac＇s equation and the relationship with classical physics, i.e. with classical field theory was established. The subject of this work is the relationship between classical relativistic physics and the quantum physics. Investigation carded out in this work, shows that the free electromagnetic field, spinor Dirac＇s field without mass, spinor Dirac＇s field with mass, and some other fields are described by the same vibrational formulation. The conditions that a field be described by Maxwell＇s equations of motion are given in this work, and some solutions of these conditions are also given. Non-relativistic approximation of the equations of the non-quantified field are the Schrōdinger＇s equations. Dirac＇s equation as a special case, contains Maxwell＇s equations and the Schrōdinger＇s equation.展开更多
It is first shown that the Dirac＇s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 x 4 relativistic time oper...It is first shown that the Dirac＇s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 x 4 relativistic time operator for spin-l/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly sma/l but non- zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli＇s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.展开更多
文摘Schrfdinger＇s equation is one the equations that mark the beginnings of the systematic quantum physics. It was shown that it follows from the Dirac＇s equation and the relationship with classical physics, i.e. with classical field theory was established. The subject of this work is the relationship between classical relativistic physics and the quantum physics. Investigation carded out in this work, shows that the free electromagnetic field, spinor Dirac＇s field without mass, spinor Dirac＇s field with mass, and some other fields are described by the same vibrational formulation. The conditions that a field be described by Maxwell＇s equations of motion are given in this work, and some solutions of these conditions are also given. Non-relativistic approximation of the equations of the non-quantified field are the Schrōdinger＇s equations. Dirac＇s equation as a special case, contains Maxwell＇s equations and the Schrōdinger＇s equation.
基金supported in part by Research Deputy of Sharif University of Technology over a sabbatical visit, hosted by the Laboratory of Photonic and Quantum Measurements (LPQM) at EPFL
文摘It is first shown that the Dirac＇s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 x 4 relativistic time operator for spin-l/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly sma/l but non- zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli＇s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.
