Pseudogap, quantum harmonic oscillation and confinement in high-temperature superconductors

For a 1-dimensional array of equidistant particles with equal masses the concepts of quantum harmonic oscillation (QHO) and particle-in-the-box (PiB) have been applied in a general form. It turns out that the lowest PiB energy level is lower than the lowest QHO energy level by E1(PiB)/E1(QHO)≈π/4. Comparing the results with experimental facts/data of high-temperature superconductors (HTSCs) might shed light on fundamental characteristics of HTSCs like the transition temperature Tc, the energy level of the superconducting state and the existence of a pseudogap ΔEpg=7.9kBTc above Tc.