Applications of The General Recursive Solution for
One-Dimensional Quantum Potential
( Theory available @ Revista Brasileira de Física and ArXiv )

	Principles of a resonant-tunneling in semiconductor devices. In this case, a barrier with a V-shaped well at the middle, similar to that created by Si delta-dopping a GaAs barrier. For each value of energy E, the figure shows a set of N (=20) wave-functions incremented in time by dt = (h/E) / N where h = 4.1357e-15 eV.s (Planck's constant). Resonance in the well occurs for E = 0.406 eV.
Wave packed representation of electrons
	An electron is being accelerated from 20eV upto 120eV by an uniform ultra-high electric field of 100V/nm. If x < xa U(x) = 0 If xa < x < xb U(x) = -U0*(x - xa)/(xb - xa) If x > xb U(x) = - U0 U0 = 100 eV, xa = 2nm, and xb = 3nm.
	Slowdown of an electron of 80eV by a restoring force If x < x0 F = 0 If x > x0 F = -k*(x-x0) k = 16eV/nm2 and x0 = 2nm.
	Reflection and transmission (tunneling) of a 40eV electron across a Lorentzian barrier. If |x-x0| < w U(x) = Umax If |x-x0| > w U(x) = Umax * w / |x-x0| Umax = 41eV, w = 0.08nm, FWHM = 4*w, and x0 = 4nm.