Classical limit of relativistic quantal system with attractive Coulomb interaction |
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Authors: | Swagata Nandi C S Shastry |
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Institution: | (1) Department of Physics, North-Eastern Hill University, 793 003 Shillong, India |
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Abstract: | Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding
to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the
expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=〈r
2〉 − 〈r〉2]1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket
in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order,
the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic
classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic
quantal system, in general. |
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Keywords: | Klein-Gordon equation for relativistic Coulomb problem coherent state for harmonic oscillator perhelion precession dispersion with time |
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