In the frame of quantummechanics, the equation to describe the particle motion in Tan2x quantum well is reducedto the hypergeometric equation. The eigenvalue and the eigefunction are obtained bysolving the Schrödinger equation. Analytical expressions of linear and thethird-order nonlinear optical refractive index changes are obtained in Tan2x quantum wellusing the density matrix formalism taking into account the intrasubband relaxation. Thelinear and the third-order nonlinear refractive index changes are calculated. The resultsshow that the refractive index changes depend on the shape of the well, the tunnelbandwith and the optical intensity. Numerical results are presented for a typicalGaAs/AlGaAs Tan2x quantum well.