{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T14:36:04Z","timestamp":1778510164735,"version":"3.51.4"},"reference-count":17,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T00:00:00Z","timestamp":1726272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e26090789","type":"journal-article","created":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T11:36:37Z","timestamp":1726486597000},"page":"789","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Evanescent Electron Wave-Spin"],"prefix":"10.3390","volume":"26","author":[{"given":"Ju","family":"Gao","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL 61801, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fang","family":"Shen","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL 61801, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,14]]},"reference":[{"key":"ref_1","unstructured":"National Academies of Sciences, Engineering, and Medicine, Sciences, D., Board, I., Board, C., Computing, C., Horowitz, M., and Grumbling, E. 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