新书推荐：David Tannor的量子力学导论

2007.10.23

前一段时间写了些不务正业的东西，Blog点击率在叫骂声中上去了。现在要谈一些有关专业科学的正经事，没多少点击也无所谓。

Bohmian Mechanics

今天以色列Weizmann研究所化学物理系（Department of Chemical Physics, Weizmann Institute of Science）的David Tannor教授在化学所做题为Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics的报告。

David的这个工作是将量子波函数的振幅折合成虚的相位因子，以规避在通常的含时量子Hamilton－Jacobi方程中的非局域作用的经典局域近似问题。作为一个实验物理化学家，我听得只是一知半解，大概只了解了一些最基本的概念，以内行的外行身份感觉这应该算是近来量子动力学研究领域比较重要的进展。有兴趣深入了解的人可以去David的主页看他们最近发表的文章。

David Tannor在Weizmann研究所的主页：http://www.weizmann.ac.il/chemphys/tannor/

Tannor教授的新书

Tannor教授提到他的这个工作是在他编写Introduction to Quantum Mechanics: A Time-Dependent Perspective一书的过程中逐渐认识到和发展出来的。他的这本书于2007年由University Science Books公司出版。

University Science Books公司网页上Introduction to Quantum Mechanics: A Time-Dependent Perspective一书的介绍和链接：http://www.uscibooks.com/tannor.htm

David告诉我这本书是在他过去的量子动力学课讲稿的基础上整理出来的。1993年我在哥大化学系时，David还是美国Notre Dame大学化学系的年轻教授。他当时在Columbia大学化学系以访问教授的身份开设了量子动力学与含时波包计算的课程。我当时也去上他的这个课，当然只是听得一知半解。当时课程的资料包括习题我回国时都带了回来，所以今天还特意拿出来给他看。他现在出的这本书有660页之巨，我猜一定比当年100多页的讲义多出了很多废话和扩充的基本量子力学内容，所以最近有机会一定要去买一本放在书架上，不能经常翻翻也要拿出来吓唬人。

国内物理化学专业学的量子力学内容中量子动力学的内容太少，Tannor的这本新书应该可以作为这方面内容的一个很好的参考。我个人推荐学习现代物理化学和化学物理的研究生和老师应该人手一本此书。我这绝不是在做广告，因为目前世界上大概也没有比David Tannor更适合去写这样一本书的人了。

Tannor教授其人

David出生和长大在纽约。他于1974-1978在Columbia大学获得化学物理专业的学士学位，1979-1983年师从Eric J. Heller(现Harvard大学物理系和化学系合聘教授)在UCLA大学化学系获得化学物理学博士学位，1983-1986年在芝加哥大学化学系跟随Stuart Rice和David Oxtoby做博士后研究。了解理论物理化学和化学物理的人应该都知道David的这几位老师都不是等闲人物。而David和他们在一起做的工作都非常有影响。比如，David和Rice教授于1985年在JCP上发表的那篇利用波包演化研究化学反应的量子控制的文章目前已被引用532次，是该领域的经典文章之一；David和Heller教授于1982年在JPC上发表的关于Raman散射的理论文章目前也被引用了466次，等等。

Rice教授1999年获得美国国家科学奖章，获奖的理由是: “For changing the very nature of modern physical chemistry through his research, teaching, a nd writing, using imaginative approaches to both experiment and theory that have inspired a new generation of scientists.”

2002年底长江三峡大坝合拢前的一个多礼拜在长江游轮上举行的国际流体与界面会议上，我恰好和Rice教授被分配在一个双人舱中一起住了好几天，向他请教了一些非常naive的问题。这个会上有很多很著名的科学家，比如说Leo Kadanoff, John Weeks，等一干人。Kadanoff是芝加哥大学物理系教授，也是1999年美国国家科学奖获得者，统计物理和非线性物理的大牛。他的获奖理由是：“For fundamental theoretical research in the areas of statistical, solid state and nonlinear physics and, in particular, for the development of scaling techniques in these fields.”我们这些人只是在国内的参加者中不算没名而已，混迹其间，相比之下绝对是小巫见大巫，提都不用提。

1987-1995年，David在大概是美国二流和三流之间的Illinois Institute of Technology和Notre Dame大学做教授，1992年获得Notre Dame大学的终身职位。出于对以色列的“热爱”（恰当的词叫做Zionism），David于1995年到以色列的Weizmann科学研究所任Associate Professor，2000年升任正教授。

我前不久说中国教授和博导很少有人能达到美国三流大学的水平，很多人很有意见。David Tannor教授的简历和工作的成绩其实正是对我的意见的一个很好的说明。在国内理论化学界目前我还没有看到有Tannor教授这样水平的人物。我的印象中也许唯有香港科技大学的严以京教授能和他有一比，严教授也做过一些相当不错的quantun control的理论研究。我相信国内理论化学界的朋友们绝不会认为我的这个评价不够公允。

顺便说一句，Tannor教授说他12岁左右就开始练武术，他和他太太的级别都是黑带（black belt），估计他们可能还是李小龙（Bruce Lee）的粉丝。

收获

Tannor教授不是我邀请来的，因为我们不算有直接关系的同行。不过我下午倒是搭便车花了一个小时左右向他介绍我们的工作和请教他自己懂得不多的理论问题，他还给我介绍了一些可能对我们的实验工作感兴趣和进行合作的国外理论学家的信息。

（今天的其它收获包括中午饭前和一个学生一起检修他的单光子计数器，在烧掉了一个几毛钱的保险丝之后我们很快确定了问题所在。另外一个学生发现她们实验中光信号检测的偏振角度有大约5度的偏离，是早上不能重复以前已经获得的那些可靠数据的原因。）

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Eric Heller教授为该书写的序言

网页链接：http://www.uscibooks.com/tannofor.htm

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, 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

 

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