The barrier penetration in the case of E=U0 has not been discussed in the current textbook of quantum mechanics.It's unreasonable to make a substitution of EU0(or EU0) for E=U0 priviously.In this paper,the penetration coefficient for the case of E=U0 is directly obtained with the help of two distinct methods.
Elementary numerical methods are used to evaluate solutions to Schrödinger’s equation for a variety of one-dimensional potential barriers and to determine the transmission coefficients of free particles. These techniques are used to study the oscillatory variations in transmission coefficients for both continuous and discontinuous potentials. The amplitude of the variations is found to be strongly increased by discontinuities in the potential function but small variations exist even for a smooth, continuous potential function. The techniques described are suitable for intermediate-level undergraduate physics students.