108
A. Lattanzi
0.0036
0.0084
0.0132
0.0180
0.0228
0.0276
0.0324
0.0372
–20
–10
0
10
20
0
10
20
30
40
50
60
Fig. 2 (ξ, τ )-contour plot of the fundamental solution of the Pearcey equation
by the NCN research project OPUS 12 no. UMO-2016/23/B/ST3/01714. I would like to thank the
two anonymous reviewers for their suggestions and comments.
References
1. Y. Nambu, Force potentials in quantum field theory. Prog. Theor. Phys. 5, 614–633 (1950)
2. E.E. Salpeter, H.A. Bethe, A relativistic equation for bound-state problems. Phys. Rev. 84,
1232–1242 (1951)
3. M. Gell-Mann, F. Law, Bound states in quantum theory. Phys. Rev. 84, 350–354 (1951)
4. E.E. Salpeter, Mass corrections to the fine structure of hydrogen-like atoms. Phys. Rev. 87,
328–343 (1952)
5. J.D. Bjorken, S.D. Drell, Relativistic Quantum Mechanics (Mc-Graw Hill, New York, 1964)
6. W. Greiner, J. Reinhardt, Quantum Electrodynamics (Springer, Berlin, 1994)
7. G.C. Wick, Properties of Bethe-Salpeter wave equations. Phys. Rev. 96, 1124–1134 (1954)
8. J. Sucher, Relativistic invariance and the square-root Klein-Gordon equation. J. Math. Phys. 4,
17–23 (1963)
9. N. Nakanishi, A general survey of the theory of the Bethe-Salpeter equation. Progr. Theor.
Phys. Suppl. 45, 1–81 (1969)
10. C. Lammerzahl, The pseudodifferential operator square root of the Klein-Gordon equation. J.
Math. Phys. 34, 3918–3932 (1993)
11. P.J. Olver, Introduction to Partial Differential Equations (Springer, New York, NY, 2014),
Chap. 8, pp. 291–338
12. W. Lucha, F.F. Schöberl, All around the spinless Salpeter equation, arXiv preprint hepph/9410221 (1994)
13. W. Lucha, F.F. Schöberl, Bound states by the Salpeter equation, arXiv prep-rint hepph/9812526 (1998)
14. D. Babusci, G. Dattoli, M. Quattromini, Relativistic equations with fractional and pseudodifferential operators. Phys. Rev. A 83(6), 062109 (2011)
A. Lattanzi
0.0036
0.0084
0.0132
0.0180
0.0228
0.0276
0.0324
0.0372
–20
–10
0
10
20
0
10
20
30
40
50
60
Fig. 2 (ξ, τ )-contour plot of the fundamental solution of the Pearcey equation
by the NCN research project OPUS 12 no. UMO-2016/23/B/ST3/01714. I would like to thank the
two anonymous reviewers for their suggestions and comments.
References
1. Y. Nambu, Force potentials in quantum field theory. Prog. Theor. Phys. 5, 614–633 (1950)
2. E.E. Salpeter, H.A. Bethe, A relativistic equation for bound-state problems. Phys. Rev. 84,
1232–1242 (1951)
3. M. Gell-Mann, F. Law, Bound states in quantum theory. Phys. Rev. 84, 350–354 (1951)
4. E.E. Salpeter, Mass corrections to the fine structure of hydrogen-like atoms. Phys. Rev. 87,
328–343 (1952)
5. J.D. Bjorken, S.D. Drell, Relativistic Quantum Mechanics (Mc-Graw Hill, New York, 1964)
6. W. Greiner, J. Reinhardt, Quantum Electrodynamics (Springer, Berlin, 1994)
7. G.C. Wick, Properties of Bethe-Salpeter wave equations. Phys. Rev. 96, 1124–1134 (1954)
8. J. Sucher, Relativistic invariance and the square-root Klein-Gordon equation. J. Math. Phys. 4,
17–23 (1963)
9. N. Nakanishi, A general survey of the theory of the Bethe-Salpeter equation. Progr. Theor.
Phys. Suppl. 45, 1–81 (1969)
10. C. Lammerzahl, The pseudodifferential operator square root of the Klein-Gordon equation. J.
Math. Phys. 34, 3918–3932 (1993)
11. P.J. Olver, Introduction to Partial Differential Equations (Springer, New York, NY, 2014),
Chap. 8, pp. 291–338
12. W. Lucha, F.F. Schöberl, All around the spinless Salpeter equation, arXiv preprint hepph/9410221 (1994)
13. W. Lucha, F.F. Schöberl, Bound states by the Salpeter equation, arXiv prep-rint hepph/9812526 (1998)
14. D. Babusci, G. Dattoli, M. Quattromini, Relativistic equations with fractional and pseudodifferential operators. Phys. Rev. A 83(6), 062109 (2011)