The Dirac Propagator for One-Dimensional Finite Square Well

DOI: 10.4236/jmp.2020.1110102   PDF   HTML     95 Downloads   261 Views  


The solution of Dirac particles confined in a one-dimensional finite square well potential is solved by using the path-integral formalism for Dirac equation. The propagator of the Dirac equation in case of the bounded Dirac particles is obtained by evaluating an appropriate path integral, directly constructed from the Dirac equation. The limit of integration techniques for evaluating path integral is only valid for the piecewise constant potential. Finally, the Dirac propagator is expressed in terms of standard special functions.

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Kongkhuntod, P. and Yongram, N. (2020) The Dirac Propagator for One-Dimensional Finite Square Well. Journal of Modern Physics, 11, 1639-1648. doi: 10.4236/jmp.2020.1110102.

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The authors declare no conflicts of interest regarding the publication of this paper.


[1] Ciftja, O. and Johnston, B. (2019) European Journal of Physics, 40, Article ID: 045402.
[2] Ewa, I.I., Howusu, S.X.K. and Lumbi, L.W. (2019) Physical Science International Journal, 22, 1-9.
[3] Al-Ani, L.A. and Abid, R.K. (2019) Al-Nahrain Journal of Science, 22, 52-58.
[4] Ewa, I.I., Lumbi, L.W. and Howusu, S.X.K. (2018) International Journal of Theoretical and Mathematical Physics, 8, 28-31.
[5] Roberts, K. and Valluri, S.R. (2017) Canadian Journal of Physics, 95, 105-110.
[6] Coulter, B.L. and Adler, C.G. (1971) Journal of American Mathematical Society, 39, 305-309.
[7] Gumbs, G. and Kiang, D. (1986) Journal of American Mathematical Society, 54, 462-463.
[8] Greiner, W. and Bromley, D.A. (2000) Relativistic Quantum Mechanics. 3rd Edition, Springer, Berlin.
[9] Nevels, R.D., Wu, Z. and Huang, C. (1993) Physical Review A, 48, 3445-3451.
[10] Janke, W. and Kleinert, H. (1979) Lettere al Nuovo Cimento, 25, 297-300.
[11] Goodman, M. (1981) Journal of American Mathematical Society, 49, 843-847.
[12] Barut, A.O. and Duru, I.H. (1988) Physical Review A, 38, 5906-5909.
[13] Riazanov, G.V. (1958) Journal of Experimental and Theoretical Physics, 6, 1107-1113.
[14] Papadopoulos, G.J. and Devreese, J.T. (1976) Physical Review D, 13, 2227-2234.
[15] Feynman, R.P. (1942) The Principle of Least Action in Quantum Mechanics. Ph.D. Thesis, Princeton University, Princeton.
[16] Feynman, R.P. Brown, L.M. and Dirac, P.A.M. (2005) Feynmans Thesis: A New Approach to Quantum Theory. World Scientific, Hackensack, NJ.
[17] Feynman, R.P. (1948) Review Modern Physics, 20, 367-387.
[18] Feynman, R.P. and Hibbs, A.R. (1965) Quantum Mechanics and Path Integrals. McGraw-Hill College, New York.
[19] Gaveau, B. and Schulman, L.S. (2000) Annals of Physics, 284, 1-9.
[20] Rosen, G. (1983) Physical Review A, 28, 1139-1140.
[21] Naimark, M.A. and Stern, A.I. (1982) Theory of Group Representation. Springer, Berlin, Heidelberg.
[22] Suzuki, T. (1977) Communications in Mathematical Physics, 57, 193-200.
[23] Wilcox, R.M. (1967) Journal of Mathematical Physics, 8, 962-982.
[24] Grosche, C. and Steiner, F. (1997) Handbook of Feyman Path Integrals. Springer-Verlag, Berlin.
[25] Bogoliubov, N.N. and Shirkov, D.V. (1959) Introduction to Quantized Fields. Wiley, New York, 147-150.

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