Kinematic properties of the Pauli equation

Abstract

Based on the Wigner-Vlasov formalism, this paper investigates the kinematic properties of the Pauli equation. It is shown that the probability current associated with the Pauli equation can be represented as a superposition of two currents with certain expansion coefficients. Each of these currents corresponds to a particular component of the spinor. The expansion coefficients effectively serve as weighting functions that determine the probability contribution of the corresponding spinor component. Therefore, each spin projection corresponds to its own probability flux. A new system of the Hamilton-Jacobi equations and also a system of motion equations in electromagnetic fields are obtained, taking into account the interaction between the spin and the magnetic field. To illustrate how these equations can be applied we have investigated the quantum system kinematics in detail using an exact solution of the Pauli equation in the presence of a uniform magnetic field and an asymmetric quadratic potential.

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BibTeX RIS

BibTeX

@misc{perepelkin2026kinematic,
  title = {{Kinematic properties of the Pauli equation}},
  author = {E. E. Perepelkin and B. I. Sadovnikov and N. G. Inozemtseva and V. A. Svetovidov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.17548},
  eprint = {2606.17548},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.17548},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Kinematic properties of the Pauli equation
AU  - E. E. Perepelkin
AU  - B. I. Sadovnikov
AU  - N. G. Inozemtseva
AU  - V. A. Svetovidov
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2606.17548
UR  - https://arxiv.org/abs/2606.17548
AB  - Based on the Wigner-Vlasov formalism, this paper investigates the kinematic properties of the Pauli equation. It is shown that the probability current associated with the Pauli equation can be represented as a superposition of two currents with certain expansion coefficients. Each of these currents corresponds to a particular component of the spinor. The expansion coefficients effectively serve as weighting functions that determine the probability contribution of the corresponding spinor component. Therefore, each spin projection corresponds to its own probability flux. A new system of the Hamilton-Jacobi equations and also a system of motion equations in electromagnetic fields are obtained, taking into account the interaction between the spin and the magnetic field. To illustrate how these equations can be applied we have investigated the quantum system kinematics in detail using an exact solution of the Pauli equation in the presence of a uniform magnetic field and an asymmetric quadratic potential.
ER  -

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