Gao Ju, Shen Fang
Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL 61801, USA.
Entropy (Basel). 2024 Sep 14;26(9):789. doi: 10.3390/e26090789.
This study demonstrates the existence of an evanescent electron wave outside both finite and infinite quantum wells by solving the Dirac equation and ensuring the continuity of the spinor wavefunction at the boundaries. We show that this evanescent wave shares the spin characteristics of the wave confined within the well, as indicated by analytical expressions for the current density across all regions. Our findings suggest that the electron cannot be confined to a mathematical singularity and that quantum information, or quantum entropy, can leak through any quantum confinement. These results emphasize that the electron wave, fully characterized by Lorentz-invariant charge and current densities, should be considered the true and sole entity of the electron.
本研究通过求解狄拉克方程并确保旋量波函数在边界处的连续性，证明了在有限和无限量子阱之外存在倏逝电子波。我们表明，如所有区域电流密度的解析表达式所示，这种倏逝波具有阱内受限波的自旋特性。我们的研究结果表明，电子不能被限制在数学奇点上，并且量子信息或量子熵可以通过任何量子限制泄漏。这些结果强调，由洛伦兹不变电荷和电流密度完全表征的电子波应被视为电子的真实且唯一实体。
