Variational Method Applied to Schrödinger-Like Equation

  • Elso Drigo Filho
  • Regina M. RicottaEmail author
  • Natália F. Ribeiro
Part of the CRM Series in Mathematical Physics book series (CRM)


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.


Variational 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.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Elso Drigo Filho
    • 1
  • Regina M. Ricotta
    • 2
    Email author
  • Natália F. Ribeiro
    • 3
  1. 1.Instituto de BiociênciasLetras e Ciências Exatas, IBILCE-UNESPSão José do Rio PretoBrazil
  2. 2.Faculdade de Tecnologia de São PauloFATEC/SP-CEETEPSSão PauloBrazil
  3. 3.Centro Universitário do Norte PaulistaUNORPSão José do Rio PretoBrazil

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