Abstract
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.
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J.J. Sakurai, Modern Quantum Mechanics Revised Edition (Addison-Wesley, Reading, 994)
E. Drigo Filho, R.M. Ricotta, Morse potential energy spectra through the variational method and supersymmetry. Phys. Lett. A 269, 269–276 (2000)
E. Drigo Filho, R.M. Ricotta, Induced variational method from supersymmetric quantum mechanics and the screened Coulomb potential. Mod. Phys. Lett. A 15, 1253–1259 (2000)
E. Drigo Filho, R.M. Ricotta, Supersymmetric variational energies of 3d confined potentials. Phys. Lett. A 320, 95–102 (2003)
N.F. Ribeiro, E. Drigo Filho, Thermodynamics of a Peyrard Bishop one-dimensional lattice with on-site hump potential. Braz. J. Phys. 41, 195–200 (2011)
I.N. Levine, Quantum Chemistry (Prentice Hall, Englewood, 2013)
T. Dauxois, M. Peyrard, A.R. Bishop, Entropy-driven DNA denaturation. Phys. Rev. E 47, R44–R47 (1993)
D.J. Scalapino, M. Sears, R.A. Ferrel, Statistical mechanics of one-dimensional Ginzburg–Landau fields. Phys. Rev. B 6, 3409–3416 (1972)
M. Peyrard, Nonlinear dynamics and statistical physics of DNA. Nonlinearity 17, R1–R40 (2004)
A. de Souza Dutra, C.A.S. de Almeida, Exact solvability of potentials with spatially dependent effective masses. Phys. Lett. A 275, 25–30 (2000)
O. Mustafa, S. Habib Mazharimousavi, Ordering ambiguity revisited via position dependent mass pseudo-momentum operators. Int. J. Theor. Phys. 46(7), 1786–1796 (2007)
J. Garcia-Martinez, J. Garcia-Ravelo, J.J. Peña, A. Schulze-Halberg, Exactly solvable energy-dependent potentials. Phys. Lett. A 373, 3619–3623 (2009)
A. Schulze-Halberg, O. Yesiltas, Generalized Schrödinger equations with energy-dependent potentials: formalism and applications. J. Math. Phys. 59, 113503 (2018)
G.R.P. Borges, E. Drigo Filho, R.M. Ricotta. Phys. A 389, 3892–3899 (2010)
Acknowledgement
EDF would like to thank FAPESP (Proc. No. 2017/01757-9) for partial support.
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Filho, E.D., Ricotta, R.M., Ribeiro, N.F. (2019). Variational Method Applied to Schrödinger-Like Equation. In: Kuru, Ş., Negro, J., Nieto, L. (eds) Integrability, Supersymmetry and Coherent States. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-20087-9_12
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DOI: https://doi.org/10.1007/978-3-030-20087-9_12
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