Question: What gives the potential in that case?
About the article "Quantum mechanics", section "Step potential".

Candidate passages:
If a point charge "Q" is placed at r=0 in a solid, what field will it produce, taking electron screening into account?One seeks a self-consistent solution to two equations:  The Thomas–Fermi screening formula gives the charge density at each point r as a function of the potential formula_15 at that point.
The Poisson equation (derived from Gauss's law) relates the second derivative of the potential to the charge density.
For the nonlinear Thomas-Fermi formula, solving these simultaneously can be difficult, and usually there is no analytical solution.
However, the linearized formula has a simple solution: formula_16 (cgs-Gaussian) With "k"0=0 (no screening), this becomes the familiar Coulomb's law.
Note that there may be dielectric permittivity "in addition to" the screening discussed here; for example due to the polarization of immobile core electrons.
In that case, replace "Q" by "Q"/ε, where ε is the relative permittivity due to these other contributions. 
The Heaviside step potential mainly serves as an exercise in introductory quantum mechanics, as the solution requires understanding of a variety of quantum mechanical concepts: wavefunction normalization, continuity, incident/reflection/transmission amplitudes, and probabilities.
A similar problem to the one considered appears in the physics of normal-metal superconductor interfaces.
Quasiparticles are scattered at the pair potential which in the simplest model may be assumed to have a step-like shape.
The solution of the Bogoliubov-de Gennes equation resembles that of the discussed Heaviside-step potential.
In the superconductor normal-metal case this gives rise to Andreev reflection. 
In a wrongful adoption case, the plaintiffs are adoptive parents of an unhealthy child, who claims that the adoption agency failed to disclose facts necessary for the plaintiffs to make an informed decision about what child to adopt, such as the background, health or genetic status of potential adoptees. 
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Aristotle gives his most substantial account of the passive intellect ("nous pathetikos") in "De Anima (On the Soul"), Book III, chapter 4.
In Aristotle's philosophy of mind, the passive intellect "is what it is by becoming all things."
By this Aristotle means that the passive intellect can potentially become anything by receiving that thing's intelligible form.
The active intellect ("nous poietikos") is then required to illuminate the passive intellect to make the potential knowledge into knowledge in act, in the same way that light makes potential colors into actual colors.
The analysis of this distinction in is very brief, and it has led to dispute as to what it means.