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Supersymmetric Dirac Equation, The: The Application To Hydrogenic Atoms (Hardcover, New)
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Supersymmetric Dirac Equation, The: The Application To Hydrogenic Atoms (Hardcover, New)
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The solution of the Dirac equation for an electron in a Coulomb
field is systematically treated here by utilizing new insights
provided by supersymmetry.It is shown that each of the concepts has
its analogue in the non-relativistic case. Indeed, the
non-relativistic case is developed first, in order to introduce the
new concepts in a familiar context. The symmetry of the
non-relativistic model is already present in the classical limit,
so the classical Kepler problem is first discussed in order to
bring out the role played by the Laplace vector, one of the central
concepts of the whole book. Analysis of the concept of eccentricity
of the orbits turns out to be essential to understanding the
relation of the classical and quantum mechanical models.The
opportunity is taken to relive the great moments of physics: From
Kepler's discovery of the laws of motion of the planets, the
development is traced through the Dirac equation up to modern
advances, which bring the concepts of supersymmetry to bear on the
derivation of the solutions.
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