Time‐Dependent Free‐Particle Salpeter Equation: Numerical and Asymptotic Analysis in the Light of the Fundamental Solution |
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| Authors: | Amalia Torre Ambra Lattanzi Decio Levi |
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| Institution: | 1. ENEA FSN‐FUSPHYS‐TSM, Italy;2. ENEA guest;3. Dipartimento di Matematica e Fisica, Universita' degli Studi Roma Tre, 00146 Rome, Italy |
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| Abstract: | A detailed study of the spinless (1+1)D free‐particle Salpeter equation is presented. It involves several aspects of the topic: from the analysis of the behavior of solutions of the equation, both numerically evaluated and asymptotically approximated for definite initial conditions, to the comparison with the behavior of the corresponding solutions of the Schrödinger equation in order to both highlight the differences and to possibly understand how the latter “flow” in the former. Interesting analogies with other fields of physics, in particular with optics, are suggested. |
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| Keywords: | Relativistic wave equations Salpeter equation Pearcey function Cuspoid canonical integrals Photonic lattices |
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