Foreword
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