  We present an asymmetric step-barrier potential for which the one-dimensional
stationary Schr\"odinger equation is exactly solved in terms of the confluent
hypergeometric functions. The potential is given in terms of the Lambert
-function, which is an implicitly elementary function also known as the product
logarithm. We present the general solution of the problem and consider the
quantum reflection at transmission of a particle above this potential barrier.
Compared with the abrupt-step and hyperbolic tangent potentials, which are
reproduced by the Lambert potential in certain parameter and/or variable
variation regions, the reflection coefficient is smaller because of the lesser
steepness of the potential on the particle incidence side. Presenting the
derivation of the Lambert potential we show that this is a four-parametric
sub-potential of a more general five-parametric one also solvable in terms of
the confluent hypergeometric functions. The latter potential, however, is a
conditionally integrable one. Finally, we show that there exists one more
potential the solution for which is written in terms of the derivative of a
bi-confluent Heun function.
