Researching Quantum Mechanics and the Schrödinger Equation!
by Valerio Raganelli , SSP-2000
(November 2005)
When I was in school, I liked very much mathematics, in particular geometry. I chose with enthusiasm to graduate in Physics at Rome University. Upon graduating, I got involved with some projects at the Instituto Nazionale di Geofisica, and was lucky to start working at the European Space Agency in 1987, but not really as a scientist. I deal today mainly with procuring policy and administration for the Agency. I never stopped studying physics though, and still work actively on some theories with European colleagues. In 2000, I participated to the ISU summer Session, which convinced that my passion for Physics and Mathematics was still very much alive...
Quantum Mechanics: The Best Way to Understand the Very-Very Small and the Very-Very Fast
The use of quantum mechanics contributes today in explaining many of the features of our world. Quantum mechanics is currently the best theory now available to human kind to describe the matter and radiation, at atomic and subatomic levels. It complements classical physics (developed by Galileo Galilei, Isaac Newton, etc.) and the relativity theory, which cannot always explain what happens to the very-very small elements (atoms, particles) and the very-very fast phenomena (speed of light).
Historically, the work of many researchers during the first half of the 20th century form the basis for quantum mechanics. They include great minds like Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli and others. Some fundamental aspects of the theory are still actively studied.
Application-wise, much of our modern technology operates at a scale where quantum effects are significant. Examples include the laser, the transistor, the electron microscope, and magnetic resonance imaging. Without quantum mechanics, there would not be postage-stamp-size computers doing billions of calculations in a milli-second! And even today, several laboratories are looking at tomorrow's applications, like for instance at how to teleport an object.
Quantum Mechanics and the Schrödinger equation
I am particularly fascinated by Erwin Schrödinger's work. He was an Austrian physicist who won the Nobel Prize for Physics in 1933, and he developed a theory providing a matrix-based framework for performing quantum mechanical calculations. His equation known as "the Schrödinger equation" contributes in solving a great number of problems in quantum mechanics. Schrödinger also wrote dozens of papers on a variety of topics, including the problem of unifying gravitation and electromagnetism, which also absorbed Einstein and which is still unsolved.
The complex equation represents a mathematical summary of quantum mechanics' very essence, and it is so effective that Enrico Fermi, an italian Nobel prize winner in Physics (1938) is told to have stated once with admiration and a smile: “The Schrödinger equation has no business in being so successful!” Of course, the equation does not solve everything, but it certainly helps. It describes the behavior of quantum particles by means of waves.
My research and the ISU experience
While working at ESA, I used my spare time to study further with colleagues the role of elastic waves. In quantum mechanics, the state of a physical system is indeed described by a "wave function". The key idea was to apply a constructive, very general and analytical solution method for the Schrödinger equation to solve the problem of N dynamically interacting bodies.
In 2000, I was lucky to participate to the ISU Summer Session, taking place in Valparaiso, Chile. It was a great experience, allowing me to meet dozens of specialists from different disciplines and different countries, and discuss at length some theories.
Re-energised, I went back to work and my proposal of analytical solutions of the Schrödinger equation was published in 2004, in the peer reviewed Proceedings of the Mathematical Institute of the Academy of Science of Bielorussia. Later in May 2005, I published a book with a young Italian colleague Luciano Giallombardo on our research on the Schrödinger equation (see picture). A first chapter deals with the analytical foundations, a second chapter goes over comments about physics and the numerical work obviously needed for every specific application, and a third chapter deals with the classical limit case. This book should be of interest to people keen on mathematics and physics, especially engineers and scientists looking for new ideas.
To conclude, studying quantum mechanics is a complex task, but I believe a really worthy endeavour for scientists and engineers in different disciplines - think of what the next space age could look like! For the next generation of quantum mechanics researchers, I will just quote Niels Bohr, a Danish physicist who made essential contributions to understanding atomic structure and quantum mechanics. He wrote that "if you are not confused by Quantum Physics then you haven't really understood it!"
Want to know more?
If some engineer, physicist or mathematician is looking for some intellectually stimulating reading and - above all -
she/he can read Italian (an English version might be coming in the future), he/she can contact Valerio to receive
more information about his book "Un Antico Problema" and research at
.
To learn more about quantum mechanics, you may want to check out:
Note: Some background elements and references were added to this article by Claire Jolly (MSS'99), in agreement with Valerio, to allow as many readers as possible to understand the rich history of quantum mechanics.