Path integral derivations are presented for two recently developed complex trajectory techniques for the propagation of wave packets, Complex WKB and BOMCA. Complex WKB is derived using a standard saddle point approximation of the path integral, but taking into account the h̄ dependence of both the amplitude and the phase of the intial wave function, thus giving rise to the need for complex clas...

The quantum mechanical tunnelling in a smooth symmetric double-well potential is a long-standing and well-known problem. Three methods have been proposed to calculate the energy splitting: the instanton method @1,2#, the WKB approximation @3,4# and numerical calculation @4–6#. The instanton method is helpful to understand the physical insight of quantum tunnelling, but the validity is restricte...

We study the stability and oscillation of traveling fronts in a three-component, advection-reaction biodegradation model. The three components are pollutant, nutrient , and bacteria concentrations. Under an explicit condition on the biomass growth and decay coeecients, we derive reduced, two-component, semilinear hyperbolic models through a relaxation procedure, during which biomass is slaved t...

In a recent paper by M A F Gomes and S K Adhikari(J.Phys.(B30) ,5987.(1997)), a matrix formulation of the Bohr-Sommerfeld (mBS) quantization rule has been applied to the study of bound states in one-dimensional quantum wells. They have observed that the usual Bohr-Sommerfeld (BS) and the WentzelKramers-Brillouin (WKB) quantization rules give poor estimates of the eigen energies of the two confi...

A bstract The Bogoliubov transformation in cosmological particle production can be explained by the Stokes phenomena of corresponding ordinary differential equation. calculation becomes very simple as far solution is described a special function. Otherwise, requires more tactics, where Exact WKB (EWKB) may powerful tool. Using EWKB, we discuss focusing on effect general interaction and classica...

We present multicomponent solar wind models self-consistently incorporating the contribution from dissipationless, monochromatic, hydromagnetic (with angular frequencies ω well below ion gyrofrequencies), toroidal Alfvén waves, which are coupled to the flow through the wave-induced ponderomotive forces. Protons and alpha particles are treated on an equal footing, and the wavelength is not assum...