Evolution Equation for a Joint Tomographic Probability Distribution of Spin-1 Particles

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• 作者：Ya. A. Korennoy ; V. I. Man’ko
• 关键词：Quantum tomography ; Spin tomography ; Evolution equation ; Proca equation ; Non ; negative vector portrait of state
• 刊名：International Journal of Theoretical Physics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：55
• 期：11
• 页码：4885-4895
• 全文大小：237 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Quantum Physics
  Elementary Particles and Quantum Field Theory
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9575
• 卷排序：55

文摘

The nine-component positive vector optical tomographic probability portrait of quantum state of spin-1 particles containing full spatial and spin information about the state without redundancy is constructed. Also the suggested approach is expanded to symplectic tomography representation and to representations with quasidistributions like Wigner function, Husimi Q−function, and Glauber-Sudarshan P−function. The evolution equations for constructed vector optical and symplectic tomograms and vector quasidistributions for arbitrary Hamiltonian are found. The evolution equations are also obtained in special case of the quantum system of charged spin-1 particle in arbitrary electro-magnetic field, which are analogs of non-relativistic Proca equation in appropriate representations. The generalization of proposed approach to the cases of arbitrary spin is discussed. The possibility of formulation of quantum mechanics of the systems with spins in terms of joint probability distributions without the use of wave functions or density matrices is explicitly demonstrated.