Explicit solution for a Gaussian wave packet impinging on a square barrier
نویسندگان
چکیده
The collision of a quantum Gaussian wave packet with a square barrier is solved explicitly in terms of known functions. The obtained formula is suitable for performing fast calculations or asymptotic analysis. It also provides physical insight since the description of different regimes and collision phenomena typically requires only some of the terms. PACS numbers: 03.65.-w Gaussian wave packet impinging on a square barrier 2
منابع مشابه
Emergence of exponentially small reflected waves
We study the time-dependent scattering of a quantum mechanical wave packet at a barrier for energies larger than the barrier height, in the semi-classical regime. More precisely, we are interested in the leading order of the exponentially small scattered part of the wave packet in the semiclassical parameter when the energy density of the incident wave is sharply peaked around some value. We pr...
متن کاملA Quantum Potential Description of One-Dimensional Time-Dependent Scattering From Square Barriers and Square Wells
The time-dependent scattering o f one-dimensional Gaussian wave packets of various energies incident on (1) a square potential barrier and (2) a square well is examined numerically, using the quantum potential introduced by Bohm. The time-dependent quantum potential is calculated in each case, and the results displayed on three-dimensional computer plots. The particle trajectories from differen...
متن کاملRotating Gaussian wave packets in weak external potentials
We address the time evolution of twoand three-dimensional nonrelativistic Gaussian wave packets in the presence of a weak external potential of arbitrary functional form. The focus of our study is the phenomenon of rotation of a Gaussian wave packet around its center of mass, as quantified by mean angular momentum computed relative to the wave-packet center. Using a semiclassical approximation ...
متن کاملDynamics of evanescent matter waves in negative-index media
Semi-evanescent and evanescent matter-waves produced by an atom wave packet impinging a repulsive barrier can be back-refracted and reconstructed by the application of negative-index “comoving” potential pulses. One shows that those collapses and revivals generate a matter wave confined on both sides of the barrier border (“surface matter wave”) and should be observable via the retardation of a...
متن کاملWave packet tunneling
The tunneling of Gaussian wave packets has been investigated by numerically solving the one-dimensional Schrödinger equation. The shape of wave packets interacting with a square barrier has been monitored for various values of the barrier width, height and initial width of the wave packet. Compared to the case of free propagation, the maximum of a tunneled wave packet exhibits a shift, which ca...
متن کامل