  In this article we analyze the behavior of a non-relativistic spinless
particle near the event horizon of a Schwarzschild-like black hole. In this
way, the Schr\"odinger covariant equation that describes the particle is
obtained from the Galilean covariance technique. The Schr\"odinger equation in
a Schwarzschild-like spacetime is solved analytically and its solutions are
given in terms of the confluent Heun function. As a relevant result, we
discovered that the energy levels of the particles are quantized and that the
particle does not escape to infinity. We obtain the existing transmission and
reflection coefficients for a particle and anti-particle pair at the event
horizon. We thus verify that there is no non-relativistic equivalent of Hawking
radiation.
