A relativistic 4D string is described in the framework of the covariant quantum theory first intro- duced by Stueckelberg [Helv. Phys. Acta 14, 588 （1941）], and further developed by Horwitz and Piron [Helv. Phys. Ac...A relativistic 4D string is described in the framework of the covariant quantum theory first intro- duced by Stueckelberg [Helv. Phys. Acta 14, 588 （1941）], and further developed by Horwitz and Piron [Helv. Phys. Acta 46, 316 （1973）], and discussed at length in the book of Horwitz [Relativistic Quan- tum Mechanics, Springer （2015）]： We describe the space-time string using the solutions of relativistic harmonic oscillator [J. Math. Phys. 30, 66 （1989）]. We first study the problem of the discrete string, both classically and quantum mechanically, and then turn to a study of the continuum limit, which contains a basically new formalism for the quantization of an extended system. The mass and energy spectrum are derived. Some comparison is made with known string models.展开更多
A quantum theory for a one-electron system can be developed in either Heisenberg picture or Schrodinger picture. For a many-electron system, a theory must be developed in the Heisenberg picture, and the indistinguisha...A quantum theory for a one-electron system can be developed in either Heisenberg picture or Schrodinger picture. For a many-electron system, a theory must be developed in the Heisenberg picture, and the indistinguishability and Pauli’s exclusion principle must be incorporated. The hydrogen atom energy levels are obtained by solving the Schrodinger energy eigenvalue equation, which is the most significant result obtained in the Schrodinger picture. Both boson and fermion field equations are nonlinear in the presence of a pair interaction.展开更多
文摘A relativistic 4D string is described in the framework of the covariant quantum theory first intro- duced by Stueckelberg [Helv. Phys. Acta 14, 588 （1941）], and further developed by Horwitz and Piron [Helv. Phys. Acta 46, 316 （1973）], and discussed at length in the book of Horwitz [Relativistic Quan- tum Mechanics, Springer （2015）]： We describe the space-time string using the solutions of relativistic harmonic oscillator [J. Math. Phys. 30, 66 （1989）]. We first study the problem of the discrete string, both classically and quantum mechanically, and then turn to a study of the continuum limit, which contains a basically new formalism for the quantization of an extended system. The mass and energy spectrum are derived. Some comparison is made with known string models.
文摘A quantum theory for a one-electron system can be developed in either Heisenberg picture or Schrodinger picture. For a many-electron system, a theory must be developed in the Heisenberg picture, and the indistinguishability and Pauli’s exclusion principle must be incorporated. The hydrogen atom energy levels are obtained by solving the Schrodinger energy eigenvalue equation, which is the most significant result obtained in the Schrodinger picture. Both boson and fermion field equations are nonlinear in the presence of a pair interaction.
