The case of the quantum unidimensional motion of a point particle subject to a viscous force proportional to the square of the speed of the particle is treated. Once a suitable Lagrangian has been chosen, the canonical quantization procedure is applied leading to a Schrödinger equation for quadratic friction and an arbitrary potential. The cases of an exponentially decreasing potential plus a linearly increasing term is explicitly solved.

• Received 30 June 1980

DOI:https://doi.org/10.1103/PhysRevA.23.1591