Energy levels and wave functions of ground and excited states of an exciton are calculated by the method of imaginary time. Energy levels as functions of radius of single and double wall nanotube are studied. Asymptotic behavior of energy levels at large and small values of the radius using perturbation theory and adiabatic approximation is considered. Spatially indirect exciton in semiconductor nanowire is also investigated. Experimental result from high quality reproducible ZnO nanowires grown by low temperature chemical engineering is presented. State of the art high brightness white light emitting diodes (HB-LEDs) are demonstrated from the grown ZnO nano-wires. The color temperature and color rendering index (CRI) of the HB-LEDs values was found to be (3250 K, 82), and (14000 K, 93), for the best LEDs, which means that the quality of light is superior to one obtained from GaN LEDs available on the market today. The role of VZn and Vo on the emission responsible for the white light band as well as the peak position of this important wide band is thoroughly investigated in a systematic way.