  We propose a modification in the Bethe-like ansatz to reproduce the hydrogen
atom spectrum and the wave functions. Such a proposal provided a clue to
attempt the exact quantization conditions (EQC) for the quantum periods
associated with potentials V (x) which are singular at the origin. In a
suitable limit of the parameters, the potential can be mapped to |x| potential.
We validate our EQC proposition by numerically computing the Voros spectrum and
matching it with the true spectrum for |x| potential. Thus we have given a
route to obtain the spectral solution for the one dimensional Schr\"odinger
equation involving potentials with regular singularity at the origin.
