Schrodinger-Langevin equation has been constructed for the ion-transport for K-ion channel. The stability of the solutions of this equation has been discussed under various physical situations. This will shed new ligh...Schrodinger-Langevin equation has been constructed for the ion-transport for K-ion channel. The stability of the solutions of this equation has been discussed under various physical situations. This will shed new light on the ion transport at nano-scale as well as the possibility of ion trapping and quantum information processing.展开更多
We prove that any nonrelativistic classical system must obey a statistical wave equation that is exactly the same as the Schrödinger equation for the system, including the usual “canonical quantization” and...We prove that any nonrelativistic classical system must obey a statistical wave equation that is exactly the same as the Schrödinger equation for the system, including the usual “canonical quantization” and Hamiltonian operator, provided an unknown constant is set equal to . We show why the two equations must have exactly the same sets of solutions, whereby this classical statistical theory (CST) and nonrelativistic quantum mechanics may differ only in their interpretations of the same quantitative results. We identify some of the different interpretations. We show that the results also imply nonrelativistic Lagrangian classical mechanics and the associated Newtonian laws of motion. We prove that the CST applied to a nonrelativistic rigid rotator yields spin angular momentum operators that obey the quantum commutation rules and allow both integer and half-odd-integer spin. We also note that the CST applied to systems of identical massive particles is mathematically equivalent to nonrelativistic quantum field theory for those particles.展开更多
In this work, the general nonrelativistic classical statistical theory presented in an earlier paper (J. Mod. Phys. 8, 786 (2017)) is applied in detail to the Euler angle and center-of-mass coordinates of an extended ...In this work, the general nonrelativistic classical statistical theory presented in an earlier paper (J. Mod. Phys. 8, 786 (2017)) is applied in detail to the Euler angle and center-of-mass coordinates of an extended rigid body with arbitrary distributions of mass and electric charge. Results include the following: 1) The statistical theory spin angular momentum operators are independent of the body’s morphology;2) These operators obey the usual quantum commutation rules in a non-rotating center-of-mass (CM) reference frame, but left-handed rules in a rotating body-fixed CM frame;3) Physical boundary conditions on the Euler angle wavefunctions restrict all mixed spin wavefunctions to a superposition of half-odd-integer spin eigenstates only, or integer spin eigenstates only;4) Spin s eigenfunctions are also Hamiltonian eigenfuctions only if at least two of the body’s principal moments of inertia are equal;5) For a spin s body with nonzero charge density in a magnetic field, the theory automatically yields 2s+1 coupled wave equations, valid for any gyromagnetic ratio;and 6) For spin 1/2 the two coupled equations become a Pauli-Schrödinger equation, with the Pauli matrices appearing automatically in the interaction Hamiltonian.展开更多
文摘Schrodinger-Langevin equation has been constructed for the ion-transport for K-ion channel. The stability of the solutions of this equation has been discussed under various physical situations. This will shed new light on the ion transport at nano-scale as well as the possibility of ion trapping and quantum information processing.
文摘We prove that any nonrelativistic classical system must obey a statistical wave equation that is exactly the same as the Schrödinger equation for the system, including the usual “canonical quantization” and Hamiltonian operator, provided an unknown constant is set equal to . We show why the two equations must have exactly the same sets of solutions, whereby this classical statistical theory (CST) and nonrelativistic quantum mechanics may differ only in their interpretations of the same quantitative results. We identify some of the different interpretations. We show that the results also imply nonrelativistic Lagrangian classical mechanics and the associated Newtonian laws of motion. We prove that the CST applied to a nonrelativistic rigid rotator yields spin angular momentum operators that obey the quantum commutation rules and allow both integer and half-odd-integer spin. We also note that the CST applied to systems of identical massive particles is mathematically equivalent to nonrelativistic quantum field theory for those particles.
文摘In this work, the general nonrelativistic classical statistical theory presented in an earlier paper (J. Mod. Phys. 8, 786 (2017)) is applied in detail to the Euler angle and center-of-mass coordinates of an extended rigid body with arbitrary distributions of mass and electric charge. Results include the following: 1) The statistical theory spin angular momentum operators are independent of the body’s morphology;2) These operators obey the usual quantum commutation rules in a non-rotating center-of-mass (CM) reference frame, but left-handed rules in a rotating body-fixed CM frame;3) Physical boundary conditions on the Euler angle wavefunctions restrict all mixed spin wavefunctions to a superposition of half-odd-integer spin eigenstates only, or integer spin eigenstates only;4) Spin s eigenfunctions are also Hamiltonian eigenfuctions only if at least two of the body’s principal moments of inertia are equal;5) For a spin s body with nonzero charge density in a magnetic field, the theory automatically yields 2s+1 coupled wave equations, valid for any gyromagnetic ratio;and 6) For spin 1/2 the two coupled equations become a Pauli-Schrödinger equation, with the Pauli matrices appearing automatically in the interaction Hamiltonian.
