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Spintronics

Exchange

Jean‐Philippe Ansermet

Published Jun 28, 2024• 0 citations
Publisher

Abstract

In 1927, while working in Zurich with F. London, W. Heitler used the newly established quantum mechanics to investigate the electronic structure of the hydrogen molecule. In 1941, W. Heitler became a professor at the Dublin Institute for Advanced Studies, where E. Schroedinger served as director. By 1949, W. Heitler had transitioned to the University of Zurich, where he continued his career in theoretical physics.

DOI
10.1201/9781003370017-2

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In 1927, while working in Zurich with F. London, W. Heitler used the newly established quantum mechanics to investigate the electronic structure of the hydrogen molecule. In 1941, W. Heitler became a professor at the Dublin Institute for Advanced Studies, where E. Schroedinger served as director. By 1949, W. Heitler had transitioned to the University of Zurich, where he continued his career in theoretical physics.
Erwin Schro¨dinger was born in Vienna in 1887, and, by 1927, principally as a result of his celebrated discovery of wave mechanics, he was recognized as one of the most outstanding physicists of his time. In that year he succeeded Max Planck in the prestigious chair of theoretical physics in the University of Berlin and it seemed certain that he would spend the rest of his career there, but the unsettled nature of European politics in the 1930s and 1940s resulted in him instead spending the years 1939 to 1956 in Dublin, where he was Director of the School of Theoretical Physics in the Institute for Advanced Studies from its foundation in 1940.
Quantum theory originated from the constant introduced by Max Planck in his radiation law in 1900. Later Niels Bohr used the idea of matter waves for the explanation of atomic spectra. Heisenberg gave an algebraic treatment, called matrix mechanics, while Erwin Schrödinger formulated his wave mechanics. He published the first of four papers containing the celebrated equation in the Annalen der Physik in 1927, and showed that the atomic spectra resulted from solving his wave equation for the vibrational states. Schrödinger moved from Zürich to Berlin as Planck’s successor. In the year 1933 he shared the Nobel Prize for Physics with Dirac. With Hitler’s coming to power, however, Schrödinger was outraged and decided to leave Germany to take up a fellowship in Oxford. In 1934 he was offered a permanent position at Princeton University, but he did not accept it. He took a position at the Institute for Advanced Studies in Dublin in 1938, where he stayed till his retirement in 1955.
The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed with experiment, e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect (the phenomenon of the deflection of electrons at low speeds being less than at higher speeds in atomic collisions), and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra.
The present manuscript revisits one of the earliest approaches to treating molecular systems within the Schrödinger formalism of quantum mechanics: the Heitler-London (HL) model. Originally proposed in 1927 and based on a linear combination of atomic orbitals, the HL model provided a foundational description of covalent bonds and has served as the basis for numerous variational methods. Focusing on the hydrogen molecule, we begin by revisiting the analytical calculations of the original HL model, from which the qualitative physics of bonding and antibonding states can be obtained. Subsequently, we propose including electronic screening effects directly in the original HL wave function. We then compare our proposal with variational quantum Monte Carlo (VQMC) calculations, whose trial wave function allows us to optimize the electronic screening potential as a function of the inter-proton distance. We obtain the bond length, binding energy, and vibrational frequency of the H2_22​ molecule. Beyond revisiting this foundational approach in quantum mechanics, our proposal can serve as improved input for constructing new, but still analytically simple, variational wave functions to describe dissociation or bond formation.
Abstract There is a certain similarity in the early lives of Planck and of Heisenberg [1,2]. Both had fathers who were professors at the University of Munich, both visited the Maximilians-Gymnasium in Munich, and both went to see a professor in Munich to seek advice for their studies. We have mentioned at the beginning of the Prologue how Jolly in vain tried to dissuade Planck from studying physics. Heisenberg, in his autobiographic book [3], which is devised as a series of conversations, tells us of a similar experience. In the autumn of 1920, when he was about to enter the university, his first choice was mathematics. He wanted not only to do course work but also learn about problems of current interest. This, he thought, he could do best by participating in a professor’s seminar usually reserved to advanced students and Ph.D. candidates. He asked for an interview with Lindemann , the most distinguished mathematician in Munich, who was famous for having proved that the number π is transcendental. But the old professor and the young student found no understanding, partly because Lindemann’s dog noisily interfered. The result was that Heisenberg opted for theoretical physics and went to ask Sommerfeld to be admitted to his seminar. Sommerfeld agreed. At that time Pauli, only a year older than Heisenberg, was already actively doing research under Sommerfeld. The two young men became life-long friends.