Tosio Kato's Work on Non-Relativistic Quantum Mechanics: A Brief Report

Abstract

In 2017, we celebrated the 100th anniversary of the birth of Tosio Kato (August 25, 1917–October 2, 1999), the founding father of the theory of Schrödinger operators. There was a centennial held in Tokyo in his memory and honor in September. I decided to write a review article on his work in nonrelativistic quantum mechanics (NRQM), which, as we'll see, was only part of his opus. I originally guessed it would be about 80 pages but it turned out to be more than 210! It will appear in Bull. Math. Sci. Our intrepid newsletter editor asked if I could produce a Reader's Digest version for the newsletter and that is what this is. A version of this will appear in Analysis and Operator Theory – In Honor of Tosio Kato's 100th Birthday, a volume edited by Th. M. Rassias and V. Zagrebnov to be published by Springer. Since the longer article has an over 600 item bibliography, I will not provide any detailed references here but refer the reader to the full article. The rest of this introduction will say a little about Kato's life while the next will summarize some major themes in his work. I will then describe in some depth (but less detail than in my Bull. Math. Sci. article) five topics that were among the most important of Kato's contributions to NRQM.

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