The quantum mechanical probability density and probability current density operators in the Pauli theory

TL;DR

This paper systematically constructs probability and current density operators for the Pauli equation from the Dirac model, highlighting differences from Schrödinger operators and discussing implications for boundary conditions and carrier dynamics.

Contribution

It introduces a systematic method to derive probability and current operators in Pauli theory from Dirac operators, emphasizing their differences from conventional Schrödinger operators.

Findings

Derived operators differ significantly from Schrödinger counterparts.

Generalized continuity equation includes additional source terms.

Approach applicable to multicomponent $oldsymbol{k} oldsymbol{ imes}$ p Hamiltonians in EFA.

Abstract

We present systematic construction of probability and probability current densities operators for one-band single particle Pauli equations starting from the operators in Dirac electron model within Second Quantized Approach. These operators are of importance as in probability interpretation of experimental data, so in establishing of boundary conditions. It is shown that derived operators differ significally from their convential Schrodinger-type counterparts. The generalization of continuity equation for probability density under external perturbations and physical meaning of additional source terms is discussed. The presented approach can be useful in analysis of carriers dynamics described within generic multicomponent $\vec{k} \cdot \vec{p}$ Hamiltonians in Envelope Function Approximation (EFA).