Abstract
We calculate the spectrum of eigenvalues for Dirac particles in a square-well potential of depth V 0 ≤ 0 and width a.
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References
For greater detail see W. Greiner, B. Müller, J. Rafelski: Quantum Electrodynamics of Strong Fields (Springer, Berlin, Heidelberg, New York 1985).
See W. Greiner, B. Müller: Quantum Mechanics — Symmetries, 2nd ed. (Springer, Berlin, Heidelber 1994).
See, for example, M.E. Rose: Relativistic Electron Theory (Wiley, New York, London).
This is covered in detail in W. Greiner: Quantum Mechanics — An Introduction, 3rd ed. and in W. Greiner: Quantum Mechanics — Symmetries, 2nd ed. (Springer, Berlin, Heidelberg 1994).
The irregular solutions yl are also noted in the literature as spherical Neumann functions nl.
W. Pieper, W. Greiner: Z. Phys. 218, 327 (1969).
From J. Rafelski, L. Fulcher, A. Klein: Phys. Rep. 38, 227 (1978).
The integral of normalization can be derived by a lengthy but clearly stated calculation. See W. Greiner: Quantum Mechanics — An Introduction, 3rd ed. (Springer, Berlin, Heidelberg 1994) Chap. 7 (Exercise 7.1).
For a more detailed discussion, see W. Greiner, J. Reinhardt: Quantum Electrodynamics, 2nd ed. (Springer, Berlin, Heidelberg, 1994).
See, e.g. M. Abramowitz, I.A. Stegun: Handbook of Mathematical Functions (Dover, New York 1965).
For a detailed discussion of this calculation, see M.E. Rose: Relativistic Electron Theory (Wiley, New York, London)
A relativistic many-body mechanics has been proposed by F. Rohrlich [see Annals of Physics 117, 292 (1979)]. It remains, though, to be seen if this theory can be quantized in a satisfactory way. We refer also to the Bethe—Salpeter equation, which is discussed in W. Greiner, J. Reinhardt: Quantum Electrodynamics, 2nd ed. (Springer, Berlin, Heidelberg 1994).
In particular this is discussed (with more precise calculations) in W. Greiner, J. Reinhardt: Quantum Electrodynamics, 2nd ed. (Springer, Berlin, Heidelberg 1994).
We refer to the literature. See, e.g., J.M. Eisenberg, W. Greiner: Nuclear Theory, Vol. II: Excitation Mechanisms of the Nucleus, 3rd ed. (North-Holland, Amsterdam 1988).
See: J.M. Eisenberg, W. Greiner: Nuclear Theory, Vol. I: Nuclear Models, 3rd ed. (NorthHolland, Amsterdam 1987) p. 73.
See J.M. Eisenberg, W. Greiner: Nuclear Theory, Vol. III: Microscopic theory of the nucleus, 3rd ed. (North-Holland, Amsterdam 1990).
This exercise has been worked out by W. Grabiak.
This solution also determines the energy eigenvalues for the MIT bag — see W. Greiner, B. Müller: Gauge Theory of Weak Interactions, 2nd ed. (Springer, Berlin, Heidelberg 1996)
and W. Greiner, S. Schramm, E. Stein: Quantum Chromodynamics, 2nd ed. (Springer, Berlin, Heidelberg 2000).
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Greiner, W. (2000). Dirac Particles in External Fields: Examples and Problems. In: Relativistic Quantum Mechanics. Wave Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04275-5_9
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DOI: https://doi.org/10.1007/978-3-662-04275-5_9
Publisher Name: Springer, Berlin, Heidelberg
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