A Simple Solution of the Relativistic Dirac Equation for a Particle in a Central Potential and an Example


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Abstract


In previous studies, a simple procedure for the general solution of the radial Schrödinger equation has been found for spherical symmetric potentials without making any approximation. The wave functions are always periodic. Two difficulties may be encountered: one is to solve the equation, E=U(r), where E and U(r) are the total and effective potential energies, respectively; and the other is to calculate the integral, ∫▒〖√(U(r))  dr 〗. If these calculations cannot be made analytically, it should then be performed by numerical methods. To find the energy of the ground state (minimum energy), there is no need to calculate this integral, it is sufficient to find the classical turning points, that is to solve the equation, E=U(r). We have applied this simple procedure to a lot of non-relativistic cases.  In this short article, by using this simple procedure, the relativistic Dirac equation for a particle in central potential well of any form was solved without making any approximation. It has been applied to the hydrogen-like atom and the results have been compared with the other results
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Keywords


Central Potentials; Relativistic Dirac Equation; Radial Equation; Spherical Symmetric Potential

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References


H. H. Erbil, A Simple Solution of the Time-Independent Schrödinger Equation in One Dimension and Some Applications, (2007) International Review of Physics (IREPHY), 1 (4), pp. 197-213.

H. H. Erbil, A Simple General Solution of the Radial Schrödinger Equation for Spherically Symmetric Potentials and Some Applications, (2008) International Review of Physics (IREPHY), 2 (1), pp. 1-10.

H. H. Erbil , Exact Simple Solutions of the Schrödinger Equation for Trigonometric and Hyperbolic Pöschl-Teller Potential Wells, (2012) International Review of Physics (IREPHY), 6 (2), pp. 144-152.

H. H. Erbil, T. Kunduracı, Simple Exact Solution of the Radial Schrödinger Equation for Three Axial Deformed Harmonic Oscillator Potential, (2012) International Review of Physics (IREPHY), 6 (3), pp. 269-278.

H. H. Erbil, H. Ertik, H. Şirin, T. Kunduraci, A Simple Solution of the Radial Schrödinger Equation for Spherically Symmetric Potential Wells with Infinite-Finite Sides and Some Examples, (2012) International Review of Physics (IREPHY), 6 (4), pp. 359-366.

H. H. Erbil, Simple Solution of the Radial Schrodinger Equation with Periodic Potential of Arbitrary Form, (2012) International Review of Physics (IREPHY), 6 (5), pp. 439-447.

H. H. Erbil, A. S. Selvi, T. Kunduracı, A Simple Scattering Cross-Section Calculation Method, (2013) International Review of Physics (IREPHY), 7 (3), pp. 230-238.

A. Messiah, Mécanique Quantique, Tome II, (Dunod, Paris, 1964).

V. Berestetski, E. Lifchitz, L.Pitayevski, Théorie Quantique Relativiste, (Edition MIR, Moscou, 1972).

Any Text-book of Quantum Mechanics or Atomic Physics

https://en.wikipedia.org/wiki/Hydrogen_atom#Er


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