Results coming from the study of relativistic vector mesons interacting with a constant magnetic field are examined through Johnson-Lippmann implications on one-dimensional oscillatorlike systems. We obtain specific nonrelativistic Hamiltonians showing new properties in quantum mechanics and leading to superpositions of bosons and pseudofermions. Moreover, two “potentials” are introduced and discussed in comparison with recent developments usually obtained in p=2 parasupersymmetric quantum mechanics. Pseudofermions are also examined, particularly with respect to orthofermions.