Alternative quantisation condition for wavepacket dynamics in a hyperbolic double well
| Autor: | D. Kufel, C. Figueira de Morisson Faria, H. Chomet |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Power series Differential equation Atomic Physics (physics.atom-ph) Wave packet General Physics and Astronomy FOS: Physical sciences Double-well potential 01 natural sciences 010305 fluids & plasmas Schrödinger equation Physics - Atomic Physics symbols.namesake 0103 physical sciences 010306 general physics Eigenvalues and eigenvectors Mathematical Physics Physics Quantum Physics Series (mathematics) Mathematical analysis Statistical and Nonlinear Physics Mathematical Physics (math-ph) Modeling and Simulation Phase space symbols Quantum Physics (quant-ph) |
| Popis: | We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width, which goes beyond the usual techniques applied to quasi-exactly solvable models. We map the time-independent Schr\"odinger equation onto the Heun confluent differential equation, which is solved by using an infinite power series. The coefficients of this series are polynomials in the quantisation parameter, whose roots correspond to the system's eigenenergies. This leads to a quantisation condition that allows us to determine a whole spectrum, instead of individual eigenenergies. This method is then employed to perform an in depth analysis of electronic wave-packet dynamics, with emphasis on intra-well tunneling and the interference-induced quantum bridges reported in a previous publication [H. Chomet et al, New J. Phys. 21, 123004 (2019)]. Considering initial wave packets of different widths and peak locations, we compute autocorrelation functions and Wigner quasiprobability distributions. Our results exhibit an excellent agreement with numerical computations, and allow us to disentangle the different eigenfrequencies that govern the phase-space dynamics. Comment: 23 pages, 9 figures |
| Databáze: | OpenAIRE |
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