用重整化短程势实现不连续波函数
Realizing Discontinuous Wave Functions with Renormalized Short-Range Potentials
摘要：
结果表明，在距离消失的直线上由三个狄拉克δ函数组成的势，只要对δ函数强度进行适当的重整化，就能引起波函数的不连续性.这可以和通常的狄拉克δ一起作为一个积木来构建最一般的三参数点相互作用族，它允许波函数的不连续性和不对称性，作为一维量子力学中自伴局域算符的零尺寸极限。实验实现的诺依曼边界进行了讨论。关键词：点相互作用，自伴延拓，$δ'$势，波函数不连续性，诺依曼边界PACS编号：3.65.- w，11.10.Gh，68.65+g
英文摘要：
It is shown that a potential consisting of three Dirac's delta functions on the line with disappearing distances can give rise to the discontinuity in wave functions with the proper renormalization of the delta function strength. This can be used as a building block, along with the usual Dirac's delta, to construct the most general three-parameter family of point interactions, which allow both discontinuity and asymmetry of the wave function, as the zero-size limit of self-adjoint local operators in one-dimensional quantum mechanics. Experimental realization of the Neumann boundary is discussed. KEYWORDS: point interaction, self-adjoint extension, $δ'$ potential, wave function discontinuity, Neumann boundary PACS Nos: 3.65.-w, 11.10.Gh, 68.65+g
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