Issue |
EPL
Volume 147, Number 4, August 2024
|
|
---|---|---|
Article Number | 44002 | |
Number of page(s) | 5 | |
Section | Nuclear and plasma physics, particles and fields | |
DOI | https://doi.org/10.1209/0295-5075/ad6eb5 | |
Published online | 29 August 2024 |
Solving the spectral problem via the boundary approximation in
theory
1 School of Space Science and Physics, Shandong University at Weihai - Weihai, 264209, China
2 Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, Institute of Space Sciences, Shandong University - Weihai, 264209, China
Received: 19 April 2024
Accepted: 13 August 2024
In theory, the resonance scattering structure is triggered by the so-called delocalized modes trapped between the
pair. The frequencies and configurations of such modes depend on the
half-separation a, which can be derived from the Schrödinger-like equation. We propose to use the boundary conditions to connect the half-localized and delocalized modes, and use boundary approximation (BA) to solve the spectrum analytically. In detail, we derive the explicit form of frequencies, configurations and spectral wall locations of the delocalized modes. We test the analytical prediction with the numerical simulation of the Schrödinger-like equation, and obtain astonishing agreement between them at the long separation regime.
© 2024 EPLA
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