Variational Method Applied to Schrödinger-Like Equation
In this work we propose to adapt the variational method to analyze a specific equation derived from a statistical model for the DNA molecule. The referred equation is a Schrödinger-like equation with an additional position-dependent function multiplying its second order derivative term. The use of the adapted variational approach is shown to be a suitable technique for the calculation of the ground state for two similar potential problems. In the first problem the additional function and the potential have an exponential position-dependence while for the second the additional function has a quadratic position-dependence and the potential has a quadratic and inverse quadratic position-dependence.
KeywordsVariational method Schrödinger-like equation Position-dependent mass Ground state solution Non-exact potential Energy-dependent potential
EDF would like to thank FAPESP (Proc. No. 2017/01757-9) for partial support.