论文标题
不相容的库仑汉密尔顿扩展
Incompatible Coulomb hamiltonian extensions
论文作者
论文摘要
我们重新审视用库仑$λ$/| x |的一维Schrödingerhamiltonian的分辨率。潜在的。我们在其自我伴侣扩展中检查与物理保护定律兼容的那些延伸。在一维半无限情况下，我们表明它们在有吸引力的情况下在u（1）圆圈上分类为u（1）圆圈（r，$ \ infty $），在排斥性的情况下。在一维无限情况下，我们通过研究本征函数的连续性找到了特定的原始分类。在所有情况下，不同的扩展与另一个扩展相关。对于具有有吸引力的潜力的实际实验，可以使用界频谱来区分哪个延伸是正确的。
We revisit the resolution of the one-dimensional Schrödinger hamiltonian with a Coulomb $λ$/|x| potential. We examine among its self-adjoint extensions those which are compatible with physical conservation laws. In the one-dimensional semi-infinite case, we show that they are classified on a U(1) circle in the attractive case and on (R,$\infty$) in the repulsive one. In the one-dimensional infinite case, we find a specific and original classification by studying the continuity of eigenfunctions. In all cases, different extensions are incompatible one with the other. For an actual experiment with an attractive potential, the bound spectrum can be used to discriminate which extension is the correct one.
