Introduction to Quantum Mechanics

A Time-Dependent Perspective

David Tannor
Weizmann Institute of Science


The importance of the time dependent formulation of quantum mechanics is evident to theorists and experimentalists alike, but this wasn't always so. Even though Schroedinger's time dependent equation was the birth of modern quantum theory, and even though Schroedinger knew about the harmonic oscillator coherent states and their classical-  like motion, attention quickly turned to the time independent Schroedinger equation. There were good reasons for this: physics was  focused on line spectra and their predictions, and for this purpose the time dependent formulation is indirect. Tradition quickly grow  around this chronology, so that textbooks often begin with the time dependent Schroedinger equation or introduce it in Chapter 1, only to drop it like a hot potato for the remainder of the book, with the   exception perhaps of a cameo appearance in the derivation of Fermi's  Golden Rule.

Now the advent of explicitly time dependent experiments, and especially the thrust toward many body systems (where computational and experimental requirements mean that no eigenstates can be found or measured, or ever needs to be measured, beyond at most the first few) makes it imperative that students see time dependence put to   good use as soon as possible.  Indeed even in the heyday of line spectra the abandonment of the time dependent Schroedinger  equation   was far too wide a swing of the pendulum.  It is enough of a shock for students of quantum mechanics that matter is a wave, and that   Schroedinger's wave is a probability amplitude, etc.  Adding to that shock is that quantum physics was done with still, motionless, {\it   stationary states}. Absurd questions like ``how does the particle get   past the node'' come up if one is divorced from time dependence. That teachers and textbook writers took this question seriously underscores the poverty of an education only about $H\psi = E\psi$. Using a time dependent approach, some familiar intuition is still  intact from the classical world, and the classical intuition we all have can be put to good use to understand quantum mechanics at a high level rather quickly.

The history of overemphasis on the time independent Schroedinger equation is there for anyone to see in the old textbooks.  What is shocking is that it is there for everyone to see in most of the new ones too! Such``academic momentum'' for textbook writers is a well   known phenomenon. Thankfully, David Tannor's book breaks free of   this syndrome and takes a far more balanced approach, employing time dependent and independent approaches in the appropriate circumstances.  The student of this text will come away well prepared to tackle today's explicitly time dependent experiments, and other  stationary experiments with a strong link to a simple time dependent  picture via Fourier transform. This is the fun way to learn quantum mechanics applied to molecular dynamics.

All of the pillars of  time dependent methodology are here: wave packets, correlation functions,  semiclassical methods, and numerical methods. The treatment of strong fields,  femtosecond multi-pulse control of reactions, photodissociation, and reactive scattering, all   of which are treated in the latter half of the book, are made accessible banking on classical intuition and the preparation in time dependent quantum and semiclassical methods in the first half.

My hope and expectation  is that this book is not only a new and much needed vehicle for training the current generation of students, but also the impulse required to change the momentum of textbook writers of the future, toward a balanced approach to quantum molecular dynamics.

The author says in his introduction essentially that this is the book  I promised to write, but never did. He is half right: I promised to write a book, but the one I planned would not have been as good as this one, nor as comprehensive.

Eric Heller
Harvard University