We introduce the Hill-Wheeler equation as a quantum mechanical distribution function for nuclear fission, replacing the conventional Fermi-Dirac distribution function of the Fermi gas model. Our model treats fission fragments as harmonic oscillators without adjustable parameters. Through calculations using experimental data on nuclear fission product charge distributions, we found that the effective fission distance is proportional to the product of fragment charge numbers, and the compound nucleus possesses different effective fission barrier corrections for each constituent element. Comparing calculated effective nuclear fission barrier corrections with neutron separation energies showed good agreement with experimental nuclear fission cross-sections, demonstrating our model’s accuracy in describing nuclear fission characteristics.