Note: The three volumes are not sequential but rather independent of
each other and largely self-contained.Basic Matters is a first
introduction to quantum mechanics that does not assume any prior
knowledge of the subject. The emphasis is on the general structure as
the necessary foundation of any understanding. Starting from the
simplest quantum phenomenon, the Stern-Gerlach experiment with its
choice between two discrete outcomes, and ending with one-dimensional
continuous systems, the physical concepts and notions as well as the
mathematical formalism of quantum mechanics are developed in successive,
manageable steps. The presentation is modern inasmuch as the natural
language of the trade - Dirac's kets and bras and so on - is introduced
early, and the temporal evolution is dealt with in a picture-free
manner, with Schrödinger's and Heisenberg's equations of motion side by
side and on equal footing.The reader of Simple Systems is not expected
to be familiar with the material in Basic Matters, but should have the
minimal knowledge of a standard brief introduction to quantum mechanics
with its typical emphasis on one-dimensional position wave functions.
The step to Dirac's more abstract and much more powerful formalism is
taken immediately, followed by reviews of quantum kinematics and quantum
dynamics. The important standard examples (force-free motion, constant
force, harmonic oscillator, hydrogen-like atoms) are then treated in
considerable detail, whereby a nonstandard perspective is offered
wherever it is deemed feasible and useful. A final chapter is devoted to
approximation methods, from the Hellmann-Feynman theorem to the WKB
quantization rule.Perturbed Evolution has a closer link to Simple
Systems than that volume has to Basic Matters, but any reader familiar
with the subject matter of a solid introduction to quantum mechanics -
such as Dirac's formalism of kets and bras, Schrödinger's and
Heisenberg's equations of motion, and the standard examples that can be
treated exactly, with harmonic oscillators and hydrogen-like atoms among
them - can cope with the somewhat advanced material of this volume. The
basics of kinematics and dynamics are reviewed at the outset, including
discussions of Bohr's principle of complementarity and Schwinger's
quantum action principle. The Born series, the Lippmann-Schwinger
equation, and Fermi's golden rule are recurring themes in the treatment
of the central subject matter - the evolution in the presence of
perturbing interactions for which there are no exact solutions as one
has them for the standard examples in Simple Systems. The scattering by
a localized potential is regarded as a perturbed evolution of a
particular kind and is dealt with accordingly. The unique features of
the scattering of indistinguishable quantum objects illustrate the
nonclassical properties of bosons and fermions and prepare the
groundwork for a discussion of multi-electron atoms.
