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In this work, we provide some simple analytical solutions to theWheeler-DeWitt equation for the minisuperspace applied to de Broglie-Bohmianquantum cosmology for particular potentials of a scalar matter field $\phi$.One solution describes a constantly rolling scalar field with a quadraticpotential plus a negative cosmological constant. The scale factor is given by aGaussian function. The other solution describes a flat Minkowski universe withthe potential of a hilltop form.

Just some simple (but nontrivial) analytical solutions for de Broglie-Bohm quantum cosmology