Solvable relativistic quantum dots with vibrational spectra

For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where the spectrum is roughly equidistant and where a fine-tuning of the levels is mediated by -symmetric interactions (composed of imaginary delta functions) which mimic creation/annihilation processes. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.