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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Semitransparent one-dimensional potential: a Green's function approach
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Semitransparent one-dimensional potential: a Green's function approach

机译:半透明的一维势:格林函数方法

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摘要

We study the unstable harmonic oscillator and the unstable linear potential in the presence of the point potential, which is the superposition of the Dirac delta(x) and its derivative delta'(x). Using the physical boundary conditions for the Green's function we derive for both systems the resonance poles and the resonance wave functions. The matching conditions for the resonance wave functions coincide with those obtained by the self-adjoint extensions of the point potentials and also by the modelling of the delta'(x) function. We find that, with our definitions, the pure b delta'(x) barrier is semi-transparent independent of the value of b.
机译:我们研究了存在点电势时的不稳定谐波振荡器和线性不稳定电势,这是狄拉克增量(x)及其导数增量'(x)的叠加。使用格林函数的物理边界条件,我们可以得出两个系统的共振极和共振波函数。谐振波函数的匹配条件与通过点电势的自伴随扩展以及通过delta'(x)函数的建模获得的条件一致。我们发现,按照我们的定义,纯b delta'(x)势垒是半透明的,与b的值无关。

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