Related papers: Wave packet tunneling
Normalized wave packets express particles in nature. Their sizes are determined by their interactions with matter, and depend on environments. Nevertheless, these characterize scatterings processes in realistic situations, and govern the…
In this paper, we reformulate the semi-classical Schr\"odinger equation in the presence of electromagnetic field by the Gaussian wave packets transform. With this approach, the highly oscillatory Schr\"odinger equation is equivalently…
A one-dimensional scattering problem off a $\delta$-shaped potential is solved analytically and the time development of a wave packet is derived from the time-dependent Schr\"odinger equation. The exact and explicit expression of the…
Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space-time background. We assume that space-time fluctuations manifest as classical fluctuations of the metric. From the non-relativistic…
We study non-relativistic propagation of Gaussian wave packets in one-dimensional Eckart potential, a barrier, or a well. In the picture used, the transmitted wave packet results from interference between the copies of the freely…
Two-particle scattering probabilities in tunneling scenarios with exchange interaction are analyzed with quasi-particle wave packets. Two initial one-particle wave packets (with opposite central momentums) are spatially localized at each…
The problem of wave packet tunneling from a parabolic potential well through a barrier represented by a power potential is considered in the case when the barrier height is much greater than the oscillator ground state energy, and the…
Nonlinear initial-boundary value problem on deep-water gravity waves of finite amplitude is solved approximately (up to small terms of higher order) assuming that the waves are generated by an initial disturbance to the water and the…
The stationary phase method is often employed for computing tunneling {\em phase} times of analytically-continuous {\em gaussian} or infinite-bandwidth step pulses which collide with a potential barrier. The indiscriminate utilization of…
Exact analytical solutions of the time-dependent Schr\"odinger equation with the initial condition of an incident cutoff wave are used to investigate the traversal time for tunneling. The probability density starts from a vanishing value…
We study the time required for a wave packet to tunnel beyond a square barrier, or to be reflected, by envisaging a physical clock which ticks only when the particle is within the barrier region. The clock consists in a magnetic moment…
Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper we explore such a scenario with one dimensional models. We adopt wave packets with…
In this work, we investigate the dynamics of the wave packet traveling through a porous semiconductor channel, with the defects being simulated by a disordered scattering region produced by obstruction potentials. The theoretical framework…
In this paper, we analyze the propagation of a wave packet through a conical intersection. This question has been addressed for Gaussian wave packets in the 90s by George Hagedorn and we consider here a more general setting. We focus on the…
In this work, we study the semi-classical limit of the Schr\"odinger equation with random inputs, and show that the semi-classical Schr\"odinger equation produces $O(\varepsilon)$ oscillations in the random variable space. With the Gaussian…
We derive a general upper bound on the spreading rate of wavepackets in the framework of Schr\"odinger time evolution. Our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically…
We present a pedagogical discussion on the time evolution of a Gaussian neutrino wave packet in free space. A common treatment is to keep momentum terms up to the quadratic order in the expansion of the energy-momentum relation so that the…
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…
Atomic wave packets in optical lattices which are both spatially finite and time-dependent exhibit many striking similarities with light pulses in photonic crystals. We analytically characterize the transmission properties of such a…
After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for…