The kinetics of nonequilibrium Bose-Einstein condensates are considered within the framework of the Gross-Pitaevskii equation. A systematic derivation is given for weak small-scale perturbations of a steady confined condensate state. This approach combines a wavepacket WKB description with the weak turbulence theory. The WKB theory derived in this paper describes the effect of the condensate on...

We prove the WKB asymptotic behavior of solutions of the differential equation −d2u/dx2 + V (x)u = Eu for a.e. E > A where V = V1 + V2, V1 ∈ L(R), and V2 is bounded from above with A = lim supx→∞ V (x), while V ′ 2(x) ∈ L(R), 1 ≤ p < 2. These results imply that Schrödinger operators with such potentials have absolutely continuous spectrum on (A,∞). We also establish WKB asymptotic behavior of s...

The paper discusses the applicability of WKB and Born (small perturbations) approximations in the problem of the backscattering of quantum particles and classical waves by one-dimensional smooth potentials with small amplitudes compared to the energy of the incident particle (above-barrier scattering). Both deterministic and random potentials are considered. The dependence of the reflection coe...

Squeezed number states for a single mode Hamiltonian are investigated from two complementary points of view. Firstly the more relevant features of their photon distribution are discussed using the WKB wave functions. In particular the oscillations of the distribution and the parity behavior are derived and compared with the exact results. The accuracy is verified and it is shown that for high p...

A new semiclassical approach to the linear and nonlinear one-dimensional Schrödinger equation is presented. For both equations our zeroth-order solutions include nonperturbative quantum corrections to the WKB solution and the Thomas-Fermi solution, thereby allowing us to make uniformly converging perturbative expansions of the wave functions. Our method leads to a new quantization condition tha...

3 WKB 17 3.

Hamiltonians whose symbols are not simply real valued, but matrix or, more generally, endomorphism valued functions appear in many places in physics, examples being the Dirac equation, multicomponent wave equations like electrodynamics in media, and Yang-Mills theories, and the Born-Oppenheimer approximation in molecular physics. Whereas the semiclassical and WKB approximation of scalar systems...

Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. While the WKB method generates an expansion in powers of h̄, the quasilinearization method (QLM) approaches the solution of the nonlinear equation obtained by casting the Schrödinger equation into the Riccati form by approximating nonlinear terms by a sequence of linear ones. It does not rely on the ex...