Step potential
The potential in that case is given by what?
Quantum mechanics
Chemical potential Electric potential Membrane potential Potential flow Gravitational potential
Chemical_potential-Chemical_potential_of_electrons_in_solids Electric_potential-In_electrostatics Membrane_potential-Other_values Potential_flow-Steady_flow Gravitational_potential-Potential_energy
Systems of particles. Chemical potential of electrons in solids. Electrons in solids have a chemical potential, defined the same way as the chemical potential of a chemical species: The change in free energy when electrons are added or removed from the system. In the case of electrons, the chemical potential is usually expressed in energy per particle rather than energy per mole, and the energy per particle is conventionally given in units of electron-volt (eV). Chemical potential plays an especially important role in semiconductor physics. For example, n-type silicon has a higher chemical potential of electrons than p-type silicon. Therefore, when p-type and n-type silicon are put into contact–called a p–n junction–electrons will spontaneously flow from the n-type to the p-type. This transfer of charge causes a "built-in" electric field, which is central to how p–n diodes and photovoltaics work. In the diode at equilibrium the chemical potential ("internal" chemical potential) varies from the p-type to the n-type side, while the total chemical potential (electrochemical potential) is constant throughout the diode. Chemical potential of electrons in solids is closely related to the concepts of work function, fermi level, electronegativity, and ionization potential. In fact, the chemical potential of an atom is sometimes said to be the negative of the atom's electronegativity. Likewise, the process of chemical potential equalization is sometimes referred to as the process of "electronegativity equalization". This connection comes from the Mulliken definition of electronegativity. By inserting the energetic definitions of the ionization potential and electron affinity into the Mulliken electronegativity, it is possible to show that the Mulliken chemical potential is a finite difference approximation of the electronic energy with respect to the number of electrons., i.e., formula_12 where "IP" and "EA" are the ionization potential and electron affinity of the atom, respectively. As described above, when describing chemical potential, one has to say "relative to what". In the case of electrons in solids, chemical potential is often specified "relative to vacuum", i.e. relative to an electron sitting isolated in empty space. This definition is somewhat delicate, however, as not all points in the vacuum are equivalent. In practice, the electrochemical potential of electrons is even more important than the chemical potential. The electrochemical potential of electrons in a solid is called the Fermi level. 
The electric potential at a point r in a static electric field E is given by the line integralwhere "C" is an arbitrary path connecting the point with zero potential to r. When the curl is zero, the line integral above does not depend on the specific path "C" chosen but only on its endpoints. In this case, the electric field is conservative and determined by the gradient of the potential:Then, by Gauss's law, the potential satisfies Poisson's equation: formula_1 where "ρ" is the total charge density (including bound charge) and ∇· denotes the divergence. The concept of electric potential is closely linked with potential energy. A test charge "q" has an electric potential energy "U"E given by formula_2 The potential energy and hence also the electric potential is only defined up to an additive constant: one must arbitrarily choose a position where the potential energy and the electric potential are zero. These equations cannot be used if the curl , i.e., in the case of a "nonconservative electric field" (caused by a changing magnetic field; see Maxwell's equations). The generalization of electric potential to this case is described below. 
From the viewpoint of biophysics, the "resting" membrane potential is merely the membrane potential that results from the membrane permeabilities that predominate when the cell is resting. The above equation of weighted averages always applies, but the following approach may be more easily visualized. At any given moment, there are two factors for an ion that determine how much influence that ion will have over the membrane potential of a cell: That ion's driving force That ion's permeability This seems to be easy to understand. If the driving force is high, then the ion is being "pushed" across the membrane hard (more correctly stated: It is diffusing in one direction faster than the other). If the permeability is high, it will be easier for the ion to diffuse across the membrane. But what are 'driving force' and 'permeability'? Driving force is the net electrical force available to move that ion across the membrane. It is calculated as the difference between the voltage that the ion "wants" to be at (its equilibrium potential) and the actual membrane potential ("E"m). So, in formal terms, the driving force for an ion = "E"m - "E"ion For example, at our earlier calculated resting potential of −73 mV, the driving force on potassium is 7 mV : (−73 mV) − (−80 mV) = 7 mV. The driving force on sodium would be (−73 mV) − (60 mV) = −133 mV. Permeability is a measure of how easily an ion can cross the membrane. It is normally measured as the (electrical) conductance and the unit, siemens, corresponds to 1 C·s−1·V−1, that is one coulomb per second per volt of potential. So, in a resting membrane, while the driving force for potassium is low, its permeability is very high. Sodium has a huge driving force but almost no resting permeability. In this case, potassium carries about 20 times more current than sodium, and thus has 20 times more influence over "E"m than does sodium. However, consider another case—the peak of the action potential. Here, permeability to Na is high and K permeability is relatively low. Thus, the membrane moves to near "E"Na and far from "E"K. The more ions are permeant the more complicated it becomes to predict the membrane potential. However, this can be done using the Goldman-Hodgkin-Katz equation or the weighted means equation. By plugging in the concentration gradients and the permeabilities of the ions at any instant in time, one can determine the membrane potential at that moment. What the GHK equations means is that, at any time, the value of the membrane potential will be a weighted average of the equilibrium potentials of all permeant ions. The "weighting" is the ions relative permeability across the membrane. 
Compressible flow. Steady flow. Potential flow theory can also be used to model irrotational compressible flow. The full potential equation, describing a steady flow, is given by: formula_8 with Mach number components formula_9 formula_10 and formula_11  where "a" is the local speed of sound. The flow velocity v is again equal to ∇"Φ", with "Φ" the velocity potential. The full potential equation is valid for sub-, trans- and supersonic flow at arbitrary angle of attack, as long as the assumption of irrotationality is applicable. In case of either subsonic or supersonic (but not transonic or hypersonic) flow, at small angles of attack and thin bodies, an additional assumption can be made: the velocity potential is split into an undisturbed onflow velocity "V∞" in the "x"-direction, and a small perturbation velocity ∇"φ" thereof. So: formula_12 In that case, the "linearized small-perturbation potential equation" — an approximation to the full potential equation — can be used: formula_13 with "M∞" = "V∞" / "a∞" the Mach number of the incoming free stream. This linear equation is much easier to solve than the full potential equation: it may be recast into Laplace's equation by a simple coordinate stretching in the "x"-direction. 
The gravitational potential ("V") is the potential energy ("U") per unit mass: formula_1 where "m" is the mass of the object. Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity. If the body has a mass of 1 unit, then the potential energy to be assigned to that body is equal to the gravitational potential. So the potential can be interpreted as the negative of the work done by the gravitational field moving a unit mass in from infinity. In some situations, the equations can be simplified by assuming a field that is nearly independent of position. For instance, in daily life, in the region close to the surface of the Earth, the gravitational acceleration can be considered constant. In that case, the difference in potential energy from one height to another is to a good approximation linearly related to the difference in height: formula_2  