We presented two methods for analytical approximation of the discrete energies in ZGNRs. Relations for the wave functions and the energy dispersion show good agreement with those obtained from numerical calculations. Our simple approximation is applicable for a wide range of ZGNR indices from N=6 to N=500. While the results show good agreement for small N-ZGNRs, the accuracy increases for wider ZGNRs. The analytical approach presented here is used to drive transition rules. Our model shows that transitions from odd to odd and even to even subband numbers are allowed and that other transitions are forbidden in ZGNRs. The model is applicable for the evaluation of optical properties of ZGNRs such as dielectric response, absorption coefficient, and energy loss spectrum.