A nonpolynomial one-dimensional quantum
potential in the form of an isotonic oscillator (harmonic oscillator
with a centripetal barrier) is studied. We provide the nonrelativistic
bound state energy spectrum En and the wave functions ψn(x)
in terms of the associated Laguerre polynomials in the framework of the
Nikiforov-Uvarov method. Under the spin and pseudospin symmetric
limits, the analytic eigenvalues and the corresponding two-component
upper- and lower-spinors of the Dirac particle are obtained in closed
form.