Quantum mechanical transforms between x- and k-space as a signal processing problem

The quantum mechanics courses usually do not discuss the transforms between coordinate- and momentum- presentations relevant to the basic quantum well tasks. If we use instead momentum p the wavenumber k=p/h then those transforms are analogous to time-dependent versus frequency-dependent transforms in classical signal processing. The paper presents numerical calculations for single and multiple quantum wells. The Heisenbergpsilas uncertainty relation validity is directly checked and the changes in spatial spectra due to increasing periodicity are discussed.