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Under certain simplifying conditions we detect monotonicity properties of theground-state energy and the canonical-equilibrium density matrix of a spinlesscharged particle in the Euclidean plane subject to a perpendicular, possiblyinhomogeneous magnetic field and an additional scalar potential. Firstly, wepoint out a simple condition warranting that the ground-state energy does notdecrease when the magnetic field and/or the potential is increased pointwise.Secondly, we consider the case in which both the magnetic field and thepotential are constant along one direction in the plane and give a genuinepath-integral argument for corresponding monotonicities of the density-matrixdiagonal and the absolute value of certain off-diagonals. Our resultscomplement to some degree results of M. Loss and B. Thaller [Commun. Math.Phys. 186 (1997) 95] and L. Erdos [J. Math. Phys. 38 (1997) 1289]

Simple diamagnetic monotonicities for Schr$ouml$dinger operators with inhomogeneous magnetic fields of constant direction