The theoretical foundation of tunneling current involves solving the Schrödinger equation for a particle in a potential barrier. The probability of tunneling, given by the transmission coefficient, depends on the height and width of the barrier and the energy of the particle. These principles are extended to condensed matter systems through the Bardeen approximation, which relates the tunneling current to the overlap of wavefunctions across the barrier. This theoretical framework allows researchers to predict and interpret tunneling phenomena in various materials, including catalysts.
