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A new ring-shaped non-spherical harmonic oscillator potential is proposed, which consists of a generalized non-harmonic oscillator potential plus an angle-dependent potential, The pseudospin symmetry for a spin- particle moving in this potential is investigated by solving the Dirac equation with an equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy equation are obtained, and the algebraic property of the energy equation and some particular cases are also discussed.

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The pseudospin symmetry for a ring-shaped non-spherical harmonic oscillator potential is investigated by solving the Dirac equation with equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy equation are obtained, the algebraic property of the energy equation and some particular cases are also discussed.

The analytical solutions to the Schrödinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov–Uvarov method, and the centrifugal term is treated approximatively with the scheme of Greene and Aldrich. The discrete spectrum is obtained and the wavefunction is expressed in terms of the Jacobi polynomial or the hypergeometric function. Some special cases of the Eckart potential are discussed for D=3, and the resulting energy equation agrees well with that obtained by other methods.