Experimental studies of potential problems in quantum mechanics using nonlinear transmission line

Abstract

The experimental method for solving the potential problem in quantum mechanics is demonstrated using the nonlinear transmission line equivalent to the Korteweg–de Vries equation (K–dV equation) Ut−6UUx+Uxxx=0. An input voltage pulse corresponding to the potential is observed to dissolve into a finite train of solitons propagating along the line. The signal voltage consisting of solitons is compared with the solution of the initial-value problem for the K–dV equation, which is exactly solved by the theory called the ‘‘inverse scattering method.’’ Consequently, it is shown that the number of bound states and discrete energy levels for one-dimensional potentials (square well potential, −U0 sech2 αx potential, and the Kronig–Penny potential) are determined by observing the signal waveform without calculations.