  We consider an elastic medium with the distortion of a circular curve into a
vertical spiral, and investigate the influence of this topological defect on
the doubly anharmonic oscillator. We show that the Schr\"odinger equation for
the doubly anharmonic oscillator in the presence of this linear topological
defect can be solved analytically. We also obtain the exact expressions for the
permitted energies of the ground state of the doubly anharmonic oscillator, and
show that the topology of the screw dislocation modifies the spectrum of energy
of the doubly anharmonic oscillator.
