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1.
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. 相似文献
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A boundS
l is given for the number of bound statesn
i in thelth partial wave corresponding to a spherically symmetric potential in non-relativistic quantum mechanics. This bound is given
by
whereV
a(l, r) is the attractive part of the effective potentialV(r)+l(l+1)/r
2. Extensive comparative study ofS
i and the Bargmann inequality is made. 相似文献
9.
Multipactor breakdown or multipactor discharge is a form of high frequency discharge that may occur in microwave components
operating at very low pressures. Some RF components of multi-channel communication satellites have co-axial geometry and handle
high RF power under near-vacuum conditions. The breakdown occurs due to secondary electron resonance, wherein electrons move
back and forth in synchronism with the RF voltage across the gap between the inner and outer conductors of the co-axial structure.
If the yield of secondary electrons from the walls of the co-axial structure is greater than unity, then the electron density
increases with time and eventually leads to the breakdown. In this paper, the current due to the oscillating electrons in
the co-axial geometry has been treated as a radially oriented Hertzian dipole. The electric field, due to this dipole, at
any point in the coaxial structure, may then be determined by employing the dyadic Green’s function technique. This field
has been compared with the field that would exist in the absence of multipactor. 相似文献
10.
Harikumar KR McNab IR Polanyi JC Zabet-Khosousi A Panosetti C Hofer WA 《Chemical communications (Cambridge, England)》2011,47(44):12101-12103
Chloropentane forms asymmetric ('A') and symmetric ('S') pairs on Si(100)-2×1, differing in the direction of curvature of one pentane tail. Surprisingly this renders the rate of thermal reaction of 'A' fifteen times greater than 'S' in chlorinating room-temperature silicon. Correspondingly, for electron-induced reaction the energy threshold for A is 1 eV less than for S. 相似文献