Low-energy DNA bubble dynamics via the quantum Coulomb potential

We developed a low-energy model that can be used at any time to describe the dynamics of deoxyribonucleic acid bubbles at temperatures below the melting point. The Schrödinger equation associated with this problem is solved in imaginary time with a quantum Coulomb potential, and we obtain an approximate expression for its more general physical solution as a linear combination of the states whose energies are close to the lower bound energy. We can then determine the probability density, the first-passage time density, and the correlation functions in terms of Bessel functions. Our findings are consistent with results obtained directly from the Fokker-Planck equation and offer a closed expression for the mentioned functions in contrast to the asymptotic results for large times previously reported for the Schrödinger framework. Comparisons with the Gamma and diffusion models are discussed.