The unperturbed Hamiltonian of quantum anharmonic oscillator is modified by introducing a simple variational scale parameter. A suitable choice of this parameter makes the eigenvalues rapidly convergent for small size of the determinant in the method of infinite Hill determinant. Simple analytic expressions for the eigenvalues are obtained by matrix diagonalization method.

Exact solutions of the potentialV(r)=−Ze²/(r+β),β>0 are obtained in theN-dimensional space for certain values ofβ by means of factorization of infinite Hill determinant. We discuss some features of the radial wave Schrödinger equation in theN-dimensional space.

A radio frequency quadrupole LINAC has been designed for the VECC-RIB project for an input beam energy of 1.0 keV/u and q/A≥1/16. The output energy will be about 90 keV/u for a 3.4 m long, 35 MHz structure. A half-scale cold model of the RFQ has been fabricated and tested for rf structure design study. The beam dynamics and rf-structure design along with the results of the cold model tests will be presented.