Quantum Mechanics Reader

by Joseph BelBruno, Dorothy Wallace

The collection of materials in this volume springs from a desire to make modern physics part of the repertoire of all scientists, indeed of all citizens of the coming century. Those of us whose lives are tied to the university cannot help but recognize the downward push of mathematics and physics into the regular curriculum of ever younger students. None of us alive now remember the time when Euclidean geometry was the epitome of undergraduate mathematics and the mark of a truly educated individual, but that was not so long ago, just the end of the last century. Now calculus has taken its place. From a historical standpoint this change is quite marvelous, representing an advance of a thousand years worth of mathematics in only a hundred years of educational progress.

For many years we have been debating the need for deeper, stronger scientific understanding. Scientific progress accelerates, and the time it takes to get up to speed in a new area is ever greater. The proud scholar of the last century with his thorough grasp of Euclid's Elements would be completely unprepared to undertake graduate studies in any scientific area. But, as a classic of human thought, the Elements were a good starting place for preparing the last century's minds for science. Now that we have a large population of undergraduates who have mastered both the calculus and a fair amount of Newtonian physics by the end of high school or the first year of college, it makes sense to ask what the scientific and mathematical classics of this century are, and how we can place them in the undergraduate curriculum in an accessible, doable way.

Surely Schrodinger's equation ranks among the classics of twentieth century thought. A thorough treatment of it embodies a large portion of the conundrums of modern physics, as well as a broad swath of the mathematics developed since Newton's calculus. Various versions of the wave equation, a little group theory, Schur's lemma and a brief mention of Gordon's solution to Hilbert's ``can you hear the shape of a drum?" problem have all insinuated their ways into this volume, riding on the coattails of Schrodinger's famous result. Discussions of the experiments leading to the formulation of quantum mechanics, as well as a development of atomic orbitals and bonding, keep the scientific situation firmly in sight at all times.

This volume is the joint work of a mathematician and a chemist, representing two very different approaches to the same question. We have made no attempt to reconcile these approaches because we feared that to do so would be to create a resource that neither scientists nor mathematicians would use in the classroom. We wanted this volume to provide the voice of the physicist and chemist in the mathematics classroom, and to provide the voice of the mathematician in the physics or chemistry classroom. The authors hope that, by keeping their own voices throughout these volumes, they can share with the reader some of the joy they feel when they practice their own craft, as well as the beauty and mystery of quantum mechanics.

These texts originally supported the third quarter of combined math-physics, which we no longer teach. They could be used in any quantum mechanics course or any mathematical methods in physics course or in a course on partial differential equations or in a senior seminar in math, physics, or chemistry.

The Belbruno texts read like straight science except there is a lot more exposition than usual, so undergraduates can actually read them. Standard treatments leave out discussion of the math, so he wrote this especially for the students in the interdisciplinary mathematics and physical science class. Wallace's Hydrogen text sounds like some weird autobiographical story and has more about Schrodinger's equation than you will see in any other undergraduate text. Students in a seminar for senior math majors really appreciate finding out why Schrodinger deserved the Nobel prize and how much math is behind it. Makin' Waves is supposed to be a readable discussion of the wave equation. Usually this equation is introduced and solved by Fourier series in two pages of text. Undergraduates stare at the text as if it is written in Arabic. It takes weeks to understand it. This version extends the discussion considerably in an epistolary novel with three voices. It is probably the only discussion of the wave equation where character development is properly considered.

At the moment all four volumes are available
TO INSTRUCTORS ONLY as pdf files.

Please contact the authors
Joseph Belbruno or Dorothy Wallace
for permission to use these materials in class.