  The spherical model for spins describes ferromagnetic phase transitions well,
but it fails at low temperatures. A quantum version of the spherical model is
proposed. It does not induce qualitative changes near the phase transition.
However, it produces a physical low temperature behavior. The entropy is
non-negative. Model parameters can be adapted to the description of real
quantum spins. Several applications are discussed. Zero-temperature quantum
phase transitions are analyzed for a ferromagnet and a spin glass in a
transversal field. Their crossover exponents are presented.
