Supersymmetry and duality in relativistic oscillator systems

► A relativistic oscillator can be mapped to a dual nonrelativistic oscillator. ► For a two-dimensional spacetime, the dual configuration space is a circle. ► The size of relativistic effects is encoded in the quantized radius of the circle. ► These two systems are related by supersymmetry to a second pair of oscillators. ► The exact wavefunctions and energies of these four intertwined systems are found.