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Physics Letters A

Transmission coefficient for a semi-classical wavepacket

R. Englman, Daniela Mugnai, Anedio Ranfagni

Published Sep 1, 1981• 2 citations
Publisher
DOI
10.1016/0375-9601(81)90229-2

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We calculate numerically the transmission coefficient and the traversal time for finite Gaussian wavepackets as a function of their widths. We consider electromagnetic waves crossing a slab and a periodic structure. We find that the periodic structure can be crossed at superluminal velocities for wavenumbers in the optical gap and sizes larger than the thickness of the system. The corresponding transmission coefficients are very small. The long wavepacket limit of the traversal time coincides with previous analytical results for the real component of the interaction time. The imaginary component of this time only affects the change in size of the wavepacket.
In the present work, we consider the transmission properties of a Gaussian wavepacket when transmits through few double and multi-slit systems in a fractional medium. For this purpose, we have solved the two-dimensional fractional Schrodinger equation utilizing a split-step Fourier method. Then, we have investigated the effects of different parameters such as the number of slits, slit width, barrier width, layer width, layer heights, fractional order, and wavepacket width on the transmission coefficient, and wavepacket evolution.
A new method is presented to introduce classical mechanics elements into the problem of obtaining the spectrum of an operator H(p,q). A finite-rank functional space is created by centring complex wavepackets on a discrete number of points on an equi-energy of the classical H(p,q) and by placing real wavepackets in the classically forbidden region. The latter span the active subspace, P, and the former the inactive subspace, Q, for an application of the method of Bloch-Horowitz. Depending on the rank retained for Q, some levels can be calculated with an extreme accuracy in a simple model while others remain evasive. A semi-classical study of the Green function in the inactive subspace Q, classically allowed, gives a clear explanation of this phenomenon and sheds new light on the significance of the semi-classical approximation for the propagator. An extension to the problem of barrier penetration is proposed.