The stationary states of the Schroodinger equation have a definite frequency and energy, and their magnitude does not depend on time - hence the name stationary. The properties of the stationary states determine the properties of wavepackets created from them.

The solution to the Schrodinger equation for piecewise constant potentials is either oscillating (E > V) or exponentially decaying (E < V). At interfaces the wavefunction and the first derivative of the wave function is continuous. Using these boundary conditions, we solve the Schrodinger equation for the case of a potential step.

If the energy of the electron is greater than the step height, there is a probability that the electron will be transmitted or reflected. The sum of the transmission and reflection probabilities is one. If the energy of the electron is less than the step height, the electron is reflected with 100% probability.