For 10 points, name this process in which a particle passes through a classically forbidden region, crossing a potential barrier higher than its total energy.
A resonant form of this phenomenon generates a quasi-local state in which a certain quantity is equal to 1 when the total energy equals the bound-state energy. One formalism describing this phenomenon produces a solution equal to a constant times momentum raised to the minus one-half power times the exponential of i over h-bar times the position integral of momentum. That formalism uses an Airy function to patch together two solutions at a turning point. Binnig and Rohrer developed a device that uses this phenomenon and a (*) scanning probe to perform nanoimaging. This phenomenon is associated with a transition from oscillatory to exponential solutions of the Schrödinger equation. For 10 points, name this process in which a particle passes through a classically forbidden region, crossing a potential barrier higher than its total energy.
A resonant form of this phenomenon generates a quasi-local state in which a certain quantity is equal to 1 when the total energy equals the bound-state energy.
quantum tunneling [in case anyone is curious: the formalism is the WKB approximation and the device is the scanning tunneling microscope]