The Salpeter Equation: Nonlocality and Pseudodifferential Operators
109
15. G. Dattoli, E. Sabia, K. Górska, A. Horzela, K.A. Penson, Relativistic wave equations: an
operational approach. J. Phys. A. Math. Theor. 48, 125203 (2015)
16. K. Kowalski, J. Rembieli` nski, The relativistic massless harmonic oscillator. Phys. Rev. A 81,
012118 (2010)
17. K. Kowalski, J. Rembieli` nski, The Salpeter equation and probability current in the relativistic
Hamiltonian quantum mechanics. Phys. Rev. A 84, 012108 (2011)
18. P. Garbaczewski, V. Stephanovich, Lévy flights and nonlocal quantum dynamics. J. Math. Phys.
54(7), 072103 (2013)
19. T. Frederico, E. Pace, B. Pasquini, G. Salmè, Generalized parton distributions of the pion in a
covariant Bethe-Salpeter model and light-front models. Nucl. Phys. Proc. Suppl. 199, 264–269
(2010)
20. T. Frederico, G. Salmè, Projecting the Bethe-Salpeter equation onto the light-front and back: a
short review. Few Body Syst. 49, 163–175 (2011)
21. T. Frederico, G. Salmè, M. Viviani, Quantitative studies of the homogeneous Bethe-Salpeter
equation in Minkowski space. Phys. Rev. D 89, 016010 (2014)
22. G. Salmè, T. Frederico, M. Viviani, Quantitative studies of the homogeneous Bethe-Salpeter
equation in Minkowski space. Few Body Syst. 55, 693–696 (2014)
23. Y. Chargui, A. Dhabbi, L. Chetouni, A. Trabelsi, Solution of the spinless Salpeter equation
with a time-dependent linear potential. Few-body Syst. 55, 1233–1243 (2014)
24. D.J. Cirilo-Lombardo, Relativistic dynamics, Green function and pseudodifferential operators.
J. Math. Phys. 57(6), 063503 (2016)
25. A. Lattanzi, Thesis, University of Roma Tre (I) (2016)
26. A. Torre, A. Lattanzi, D. Levi, Time-dependent free-particle Salpeter equation: numerical and
asymptotic analysis in the light of the fundamental solution. Ann. Phys. (Berlin) 529, 1600231
(2017)
27. A. Torre, A. Lattanzi, D. Levi, Time-dependent free-particle Salpeter equation: features of
the solutions, in Quantum Theory and Symmetries with Lie Theory and Its Applications in
Physics Volume 2, ed. by V. Dobrev. Springer Proceeding in Mathematics & Statistics, vol. 255
(Singapore, Springer, 2018), pp. 297–307
28. A. Lattanzi, D. Levi, A. Torre, The missing piece: a new relativistic wave equation, the Pearcey
equation. J. Phys. Conf. Ser. 1194(1), 012065 (2019). IOP Publishing
29. A. Lattanzi, D. Levi, A. Torre, Evolution equations in a nutshell, in Conference Proceedings
CSPM 2018 (2019)
30. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs,
and Mathematical Tables, 9th edn. (Dover Publication, Mineola, NY, 1970)
31. G. Dattoli, D. Babusci, E. Sabia, S. Licciardi, Mathematical Methods for Physicists (World
Scientific, Singapore, 2019)
32. G. Dattoli, M. Quattromini, A. Torre, Miscellaneous results on the theory of evolution operators
and generalized transforms. Nuovo Cimento Soc. Ital. Fis. Sezione B 114, 693–708 (1999)
33. G. Dattoli, D. Levi, Exponential operators and generalized difference equations, Nuovo
Cimento Soc. Ital. Fis. Sezione B 115(6), 653–662 (2000)
34. G. Dattoli, B. Germano, M.R. Martinelli, P.E. Ricci, A novel theory of Legendre polynomials.
Math. Comput. Model. 54(1–2), 80–87 (2011)
35. G. Dattoli, P.E. Ricci, D. Sacchetti, Generalized shift operators and pseudo-polynomials of
fractional order. Appl. Math. Comput. 141(1), 215–224 (2013)
36. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New
York, 2014)
109
15. G. Dattoli, E. Sabia, K. Górska, A. Horzela, K.A. Penson, Relativistic wave equations: an
operational approach. J. Phys. A. Math. Theor. 48, 125203 (2015)
16. K. Kowalski, J. Rembieli` nski, The relativistic massless harmonic oscillator. Phys. Rev. A 81,
012118 (2010)
17. K. Kowalski, J. Rembieli` nski, The Salpeter equation and probability current in the relativistic
Hamiltonian quantum mechanics. Phys. Rev. A 84, 012108 (2011)
18. P. Garbaczewski, V. Stephanovich, Lévy flights and nonlocal quantum dynamics. J. Math. Phys.
54(7), 072103 (2013)
19. T. Frederico, E. Pace, B. Pasquini, G. Salmè, Generalized parton distributions of the pion in a
covariant Bethe-Salpeter model and light-front models. Nucl. Phys. Proc. Suppl. 199, 264–269
(2010)
20. T. Frederico, G. Salmè, Projecting the Bethe-Salpeter equation onto the light-front and back: a
short review. Few Body Syst. 49, 163–175 (2011)
21. T. Frederico, G. Salmè, M. Viviani, Quantitative studies of the homogeneous Bethe-Salpeter
equation in Minkowski space. Phys. Rev. D 89, 016010 (2014)
22. G. Salmè, T. Frederico, M. Viviani, Quantitative studies of the homogeneous Bethe-Salpeter
equation in Minkowski space. Few Body Syst. 55, 693–696 (2014)
23. Y. Chargui, A. Dhabbi, L. Chetouni, A. Trabelsi, Solution of the spinless Salpeter equation
with a time-dependent linear potential. Few-body Syst. 55, 1233–1243 (2014)
24. D.J. Cirilo-Lombardo, Relativistic dynamics, Green function and pseudodifferential operators.
J. Math. Phys. 57(6), 063503 (2016)
25. A. Lattanzi, Thesis, University of Roma Tre (I) (2016)
26. A. Torre, A. Lattanzi, D. Levi, Time-dependent free-particle Salpeter equation: numerical and
asymptotic analysis in the light of the fundamental solution. Ann. Phys. (Berlin) 529, 1600231
(2017)
27. A. Torre, A. Lattanzi, D. Levi, Time-dependent free-particle Salpeter equation: features of
the solutions, in Quantum Theory and Symmetries with Lie Theory and Its Applications in
Physics Volume 2, ed. by V. Dobrev. Springer Proceeding in Mathematics & Statistics, vol. 255
(Singapore, Springer, 2018), pp. 297–307
28. A. Lattanzi, D. Levi, A. Torre, The missing piece: a new relativistic wave equation, the Pearcey
equation. J. Phys. Conf. Ser. 1194(1), 012065 (2019). IOP Publishing
29. A. Lattanzi, D. Levi, A. Torre, Evolution equations in a nutshell, in Conference Proceedings
CSPM 2018 (2019)
30. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs,
and Mathematical Tables, 9th edn. (Dover Publication, Mineola, NY, 1970)
31. G. Dattoli, D. Babusci, E. Sabia, S. Licciardi, Mathematical Methods for Physicists (World
Scientific, Singapore, 2019)
32. G. Dattoli, M. Quattromini, A. Torre, Miscellaneous results on the theory of evolution operators
and generalized transforms. Nuovo Cimento Soc. Ital. Fis. Sezione B 114, 693–708 (1999)
33. G. Dattoli, D. Levi, Exponential operators and generalized difference equations, Nuovo
Cimento Soc. Ital. Fis. Sezione B 115(6), 653–662 (2000)
34. G. Dattoli, B. Germano, M.R. Martinelli, P.E. Ricci, A novel theory of Legendre polynomials.
Math. Comput. Model. 54(1–2), 80–87 (2011)
35. G. Dattoli, P.E. Ricci, D. Sacchetti, Generalized shift operators and pseudo-polynomials of
fractional order. Appl. Math. Comput. 141(1), 215–224 (2013)
36. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New
York, 2014)