Schrödinger operators with non-Hermitian matrix-valued potentials

To formulate non-Hermitian quantum physics, it is necessary to study the mathematical apparatus for non-self-adjoint operators. Matrix-valued potentials play a role especially in involving the interaction of a particle spin with an electromagnetic field, as can be seen in the Pauli operator. Specifically, we focus on the Schrodinger operator with non-Hermitian matrix-valued potentials. The main task is to correctly define this operator as the sum of the free Hamiltonian and the potential. We derive conditions for the potential to ensure the stability of the essential spectrum. Finally, we derive an estimate of the eigenvalues in the first dimension and state a condition for the potential that excludes the existence of a point spectrum in the third dimension.