Time-Dependent Invariants for Dirac Equation and Newton-Wigner Position Operator

V. I. Man'ko; R. V. Mendes

doi:10.1088/0031-8949/56/5/001

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arXiv · quant-ph/9702035

Time-Dependent Invariants for Dirac Equation and Newton-Wigner Position Operator

V. I. Man'ko·R. V. Mendes

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Abstract

For Dirac equation, operator-invariants containing explicit time-dependence in parallel to known time-dependent invariants of nonrelativistic Schrödinger equation are introduced and discussed. As an example, a free Dirac particle is considered and new invariants are constructed for it. The integral of motion, which is initial Newton-Wigner position operator, is obtained explicitly for a free Dirac particle. For such particle with kick modeled by delta-function of time, the time-depending integral, which has physical meaning of initial momentum, is found.

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V. I. Man'ko, R. V. Mendes. 1997-02-18. Time-Dependent Invariants for Dirac Equation and Newton-Wigner Position Operator. https://doi.org/10.1088/0031-8949%2F56%2F5%2F001

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