Energy levels of two‐dimensional anharmonic oscillators with sextic and octic perturbations

Two renormalized versions of inner product and hypervirial techniques are presented together with the Hill determinant approach for performing accurate calculations of the energy levels of two‐dimensional oscillators characterized by the potentials VN=6(x, y)=(x2+y2) +λ(axxx6+ayyy6+3axyx4 y2+3ayxx2y4) and VN=8(x,y)= (x2+y2)+λ(axxx8+ayyy8+6b xyx4y4 +4axyx6y2+4ayxx2y6). The methods have been used effectively to calculate the energy eigenvalues for many eigenstates over a wide range values of perturbation parameter λ and various values of coefficients aIJ. The results produced by various techniques are compared with each other.

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