Classical limit of relativistic quantal system with attractive Coulomb interaction

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.     

A bound on the number of bound states in the Schrödinger equation

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.     

Investigation of multipactor breakdown in communication satellite microwave co-axial systems

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.