Preface
- Page ID
- 549126
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This book is designed to be a resource for those studying time-dependent quantum mechanics, dynamics, and spectroscopy of molecular systems. This text is largely for chemists: people whose view of the world is formed in the language of atoms and molecules. It is for chemistry students who are starting—like I did—without a deep knowledge of physics and math, but who find it important to understand the concepts and tools that lie outside of the traditional chemistry curriculum. However, I also hope this may be a useful reference for practitioners in the field, including those who are familiar with the content but haven’t trained with a molecular perspective. Writing for these different audiences means that the material varies between basic qualitative concepts and advanced formalism.
This is not a textbook or lecture notes or a handbook but all of these at the same time. The online format provides an opportunity to do things differently: There are no stringent constraints on length, which allows a self-contained presentation of material that doesn’t hesitate to be repetitive and permits more detail in derivations, lengthy examples, math notes, and appendices. We can incorporate video and readily link to content within the book and externally. These digital features are still somewhat limited but will grow with time.
Perhaps most importantly, this is not a static document but is regularly corrected and expanded. Since the first public release of this content as simple lecture notes on MIT’s OpenCourseWare in 2003, there have been periodic releases of new content and updates to transform what were lecture notes into a book’s narrative form. 2025 brings the first substantial release of new material since the 2014 edition, along with extensive editing of all earlier material.
In some sense, the content here draws from and curates material originating from many sources. In part these sources are recorded in the references to books, papers, and notes given throughout the text. However, the structure and scope of the content was strongly shaped by lecture notes from prior colleagues and instructors, including Bob Field, Graham Fleming, Keith Nelson, Troy Van Voorhis, and John Ross. Bob Silbey deserves a special acknowledgement, not only for giving me material when I started teaching, but for shaping my whole approach to quantum mechanics, such as his mantra: First write down the Hamiltonian… In more recent years, numerous people have offered feedback and found errors, but Sukhbir Mahajan, Ruoyu Xu, and Samuel Knight were particularly helpful. Special thanks to the many students, postdocs, and faculty who have reached out to tell me how helpful my notes were for them or point out errors; I continue this work in hopes that it may continue to be a useful resource for its readers.
Finally, I want to thank Artemie Chang, Peter Giunta, Anne Hudson, and Tanya Shpigel, for their assistance over the years with transcribing and editing the material and with preparing it for electronic distribution, the Department of Energy and National Science Foundation for their support of my research in this area, and my wife Karen for her enduring support and patience with my project.
Andrei Tokmakoff
December 2025