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Ǭסססססססססססססססססססססססססססס

̳ϵһ



ʱ211գйũӭ֮ʣʡѧԺѧϵ
ݡѧԺڣInstitute ProfessorࡤIsadore Singer
1924-2021ǣ97ղ¡ͬӢϡSinger
λ쳹ִѧԺһ
Զֹͣ˸質ѧǶĸм뻳ְǵ
ԡC֮޵٣Luciano Pavarotti1936-2007ĸм뻳һ
Ũҡ

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ϵ׫дʿ֮ʣոձϵ˹ͨMarshall Stone1903-1989Ƹ
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΢ּε˼ʱΪֹʮѧشӰ
졣

ڴӲЪǵɵһ̫˼ͥ
һͯʡѧԺѧϵͬάɣNobert Wiener
1894-1964츳ܸߵĹѧ˹ڣĸ׽һ
ӡˢˣ´½ӦǳӢ˵
ٵĴѧġͱıݾ񡢺
ڼݴѧУͬ¹ѧ˹÷Stephen Smale
1930-һЪѧѧ1944Ҵ
ҵμӶսΪ½״＼Աפڷɱʱ
޹ִγ̡ѧۡΪԼһЩ
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˵ȥҲǸȥĴɭFreeman Dyson1923-2020ڣ40
ӢŴѧʱȺ͵ˣPaul Dirac1902-1984ѧϰڹ
Godfrey Hardy1877-1947ӰԴѧҵò
ζѧŵķRichard Feynman1918-1988ɭѸ
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ϵھˣMarie Curie1867-1934йʿʩʿԪ
1908-2007ָдѧʿġάѧɭNorman 
Levinson1912-1975ʡѧԺ޶ĵרҵһֱ1934
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ǵģǽǹ档ôһڴϿܶ˼
ѧʷ˲ķ֮һ

ȣ˽һ½ǹ;ѧɭ̬ѧ湤ĿƼ
ԱȥҰ⿼ɭֵĳơġ֡Ϊˣɭ
ܺĴϸжһЩָ꣬ɭֵ
ԼٵķվͿԱôӦĹ滮ʩҲͺ֮ˡ
Щָ棬ܸBasal areaλλ꣩
ظߴ1.3ףĶ֮ͣĵһ
ָ֮һǹġ

ǽǹΪʲô˲أΪڽǹ浮֮ǰͳɭֵܸ
ҪȻһٺüƽ׵Բλ򣨽СȻ
ÿ߻Ƥ߽ظߴֱܳһ꣬
ÿظߴĺӺ֮ٳɵõܸ
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ʱҪʱ䣬ʮַʱڴʱҪõʮ׳
ƤߣһһǶɲ˵ġǹķ׸ı档

µѧ߶ءϣWalter Bitterlich1947귢˽ǹ棬
֣ܸҪͲֻҪһվĳһ
ŽǹתһȦһӾܸ㶨ǣһӵĩ
£ƬԶˣߴӽƬıԵĻһΰۣ
дγһнԶȻ峯һ򻺻תɨ
ɼÿһظߴд0ʼһɴڽǹ
ϽƬۣͼ1ϸڰۣ룩ͲӣպȣУ
ֻ0.5һܺõּΪܸɣַէһ
ʵԼʵۻģСɱĸʳۣϸ
ѧ֤Ϊϵġ÷һɹӰҲǸԵģ
áܸһޱѲָ꣬һʮײָ꣡

˼ǣֻҪ˽ǹĻ˼룬ؽǹĳߴ磨ѡ
ʵһ԰ۿǡΪǹ桱ñӡҩף
ָͷԱȻԣơƿȻǲڻ¡ÿǹ棬
Ҿͻر̾ʱһļ档

͵ܺãŮѲòڳŶӵһ
͸ʳͶܿġǶλƽֻ͸
۲࣬ȴ֪̬ѧһ͸۲ֲȷе˵
ֲĸϵоϵ̬ṹϲ˽ֲ
̬ܵȶҪ塣ֱգֲϵоԶԶͺڶ
ֲϲֵоҪԭֲĸϵ£Ĺ۲һֱ
ڲٵļƿϲ򵥺ֱӡҰԸϵ
ԭλ۲⣬ھȻǳõķھԸϵɽǿŶ
ƻԸ÷ֻϵڿռϵľֲ̬ȴ޷
ϵʱϵĶ̬仯

ҪоϵʱϵĶ̬仯Ŀǰõһװý
Rhizotronʵǽһ͸ġǲҲ
͸ϡá̶ĿֲԵϣϸ
䡰֮Ŀ϶ĸϵʱŴ
ȥ⡱˾ͿԲöñʻջɨķʽ
ЩϵĴСϸϲ¼

ᵽİʽ©ƣҲһȴһֱķ
мصĸ20ͳĵ¹ֱԲѧŵ
NollԸɭķѧ߿÷Kroemerͬʱһڽ졣
ʱǵװûСǽСϵʵҡһγ֡
ǰԺˡ˺󣬻ڸ۲ϵо
ֻ࣬ڲͬоУĳߴ仯ܴ󣬶̵ĽʮףĿɴＸ
ʮףռ䷿ôĺơµĳڸҪ
ϣԸϵŶܴˣһֶԸϵŶ
С΢MinirhizotronڽʮﱻƼȸ
ΪС΢һֳԼ0.3-2ף⾶һС10׵Բܣб
Уʹõתͷɼ¼ܱڲ360ȵĸϵͼ񡣴⣬״
ĸУRhizoboxƽ״ĸƬRhizoslideҲбԭ
ơ

ʣֹ۲ⷽкܶȱ㡣磬Ŷʼն
ڵģϾһ֣ÿβʱ仯
ȡգҲܻŸϵңڸǸƽ棬ֻ
õϵĶάռݣڵһкܶѡķǻ
֦ҶάռݡˣĿǰΪֹ޸õĹ۲ܹⷽ
ȫȡҰ⣬ҲǺε顣

˵ǣ۲ϵһʮּĹ磬Ϊоϵ
ڶϲйʱòðʮȵϺһ
׺ıѩµװиɨǶ޷ڵ¹
£ǾֶķʽЩϵһһ桢Ի
ݡöԿѧȳͶִţ֪Ŀհף
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ǵճУһЩƷǼȲʵϣҲǹ۲װ
ãֻڿлаݡҶĽɫûǣܶ๤ͻ
ά裬޷չĸߵǷǳģǲʤö١

ȫƷе̳š͡Ƶãǰ
кԤҰ⣬ܶСGPSԽķ꣬
ðȫǸѡ񣬽֮棬Ȳܷˮ
롣ֻԴӽʱԺ󣬾һֱҰ⿼зһ
ϴGPSԽָ롢ǡֵͲȹߣ
˰ȫϣźֻˮʱȫ
棬ȷˮֲӰָʮַ㡣ע⣬ʹʱҪ
ףǴףڵͷӶӰֻչ
ܣÿǰҪѰȫȥ⣬ϰȫ׵ֻò
̫ۣһҪӵ绰Ƚȥپ

ʪȶȴߣֱۡСˣ֮Ϊ˷
ֹɴˮʪ˿ڸȾɽȫ׵͹ȥڱ棬
ʱֵһӡ

ȫʵӦõҲСֲѧʱý
оֱӼƷƷ𺦡ʱһȫϼ´Ĵָ
СƬ֮ڼоߵڲࡪƳɵİȫǲĻϣ
Чо߶Ʒˡڰȫ׷ǳôռüоڲ౾
Ͳ̫ԣĿռ䣬˲ֲƷռԴϣ
żȻƳһλ̬ͬÿоѶలȫף벻Ҫ
С֣ǻǶԷ׼ġ

ܳ˱ͬȼβƣоֲͶʱǾ
õĸߡ磬ѧ̬ѧľѧDendrochronologyУ
оԱҪ׶ľڻȡоȻͨо
ѧĲܹһּ״Լһ
仯ϢоһһֱסԼʮײ
ȵСľ׶ϣҶϳɼ֮ںѷβ
װѴҶϺСλ׶Ӷݵƫȱʧ
⣬ڱоʱֻװֽУһֽˣƷ֮
ⶼҰڼ׷¹ʡʱոȡо
˳һһܺõķܽϺõر֤о˳򣨼ʹ
ҲûϵմȥͳɣϿԱעֻϵϱǩ
ӶЧƷ磬оԻζķӦΪʱ͸
ܳͨеͨѧǶй۲ͼ¼

ӲҳܹͶҹҰ̦޺飬
䶴Ѩյʱ򣬻һּõıߡҪվһƷ
ڲͬľӲҼɡصƤ߻Ӳʱ
̫Ҫֱַһ˲㡣ȻӲ
ʱᷴ⡪һȱ㡪ԽþɵӲңӲֽ

ֽܰ󿧷ȣҲ̬ʵġ͡
ֽһЩˮɰˮĹ˲һЩ
ʵ֮УΪɻȱĹߡ磬оʳԴʱõġ෨
Frass methodУֽռꡢӬ׳ķ㣺˿
ֽ©ڲͬ£ֽὫˮ˵ͬʱѧͨ
ֽڷʹСӶʳԴķḻȡ

ֽܹŮѵᣬҰ⣬ʱ̶
ֲ걾ɻȱĹߡֲĸϵǱڳ֮ʮ׶ϣ
ʧˮʱǼˮʪֽ棨ǿһЩһЩ
ģܼȱϵ˽ṹǼܲ𺦣һʱڱʪַ
ʵҲͬá

оΪСƷ˵ôϡ
ƽ΢ȴƽѧรĹӵгɫı֡
˹ؼĽɫÿѧõط˴ڣҲôڸز˿ѧ

װѣһλѧߣտȡԶĵʱ
ûҲĿѧͲǰߣһ
ߣһѧù¡һĪչʱûҲ
Ĵ𰸾Ͳߡǰ

οף

ģ
Bohm, W., 2012. Methods of studying root systems (Vol. 33). 
Springer Science & Business Media.
Goldberg, N.N. and O'Reilly, O.M., 2020. Mechanics-based model for 
the cooking-induced deformation of spaghetti. Physical Review E, 101(1), 
p.013001.
Harmon E.M. Nadelhoffer, K.J. and Blair, J.M., 1999. Measuring 
decomposition, nutrient turnover, and stores in plant litter. Standard 
soil methods for long-term ecological research, 202.
Keuskamp, J.A., Dingemans, B.J., Lehtinen, T., Sarneel, J.M. and 
Hefting, M.M., 2013. Tea Bag Index: a novel approach to collect 
uniform decomposition data across ecosystems. Methods in Ecology and 
Evolution, 4(11), pp.1070-1075. 
Krams, R., Krama, T., Brmelis, G., Elferts, D., Strode, L., 
Daukane, I., Luoto, S., mits, A. and Krams, I.A., 2021. Ecological 
traps: evidence of a fitness cost in a cavity-nesting bird. Oecologia, 
pp.1-11.
Mukerji, K.G., Manoharachary, C. and Singh, J. eds., 2006. 
Microbial activity in the rhizosphere (Vol. 7). Springer Science & 
Business Media.
Robertson, G.P., Coleman, D.C., Sollins, P. and Bledsoe, C.S. eds., 
1999. Standard soil methods for long-term ecological research (Vol. 2). 
Oxford University Press on Demand.
Rytknen, S. and Krams, I., 2003. Does foraging behaviour explain 
the poor breeding success of great tits Parus major in northern Europe?. 
Journal of Avian Biology, 34(3), pp.288-297.
Wetherington, M.T., Jennings, D.E., Shrewsbury, P.M. and Duan, J.J., 
2017. Climate variation alters the synchrony of hostCparasitoid 
interactions. Ecology and evolution, 7(20), pp.8578-8587.

վ
ѲֽͻСݳ 
https://www.sohu.com/a/333024067_119097
޿ƌWҒΗǧļO䣬DOyصĹ̼
https://www.seinsights.asia/article/3289/3270/4722
ɭôοٲͦ򵥣һĴָ͡
https://kknews.cc/news/rnjzn2v.html
 ǹ 
https://wenku.baidu.com/view/ef06f23a376baf1ffc4fadc9.html
״ʼƽ̹ʱ
https://www.ximeiapp.com/article/3199872
Entomological classics C The Tullgren (Berlese) Funnel 
https://simonleather.wordpress.com/2016/05/03/entomological-classics-t
he-tullgren-berlese-funnel/
MIT mathematicians solve age-old spaghetti mystery 
https://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-m
ystery-0813

ά:
Tullgren funnel https://en.wikipedia.org/wiki/Tullgren_funnel
Antonio Berlese https://fr.wikipedia.org/wiki/Antonio_Berlese
Walter Bitterlich https://en.wikipedia.org/wiki/Walter_Bitterlich
Proportionator 
https://en.wikipedia.org/wiki/Proportionator#Plotless_sampling
Angle gauge https://en.wikipedia.org/wiki/Angle_gauge



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µ仯滷˾޴Ӱ졣
ģͳл輫ظı˵رͿ֮ˮ
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Եĺϼڻȫƽ߶ߣغ
бͣʧĸɽҪӵˮɺˮʹ
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ȫ仯ܵӰ졣

Щ޴Ӱ죬ȫ仯˼ĹעΪ
һŵĻ֮һ ƵƵýͷѡٵı
֮С仯ҲΪҺ͹֯صоĿ2021꣬ŵ
ίһνѧоĿѧSyukuro Manabe  Klaus 
HasselmannǶ˽仯ԼӰ
ԵĹסΰ佱һٽǶȫ仯Ĺע

仯ϵͳӦĳʱڻ۵Ľ
ϵͳȻ仯 ӦķȺСˣҪߣϵͳ
гھȷĹ۲ز١֪ٶǰһλסӢ׶ص
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ĳڴ¶ݵıȽϣһöĽؽʾ˳л
Ӱ졣ǱҪܵ仯о¬ˡ Luke 
Howard

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1772ӢʱǿѧӢչʱ 
ţ١ڡġ˹ȿѧ޽ѧ֪ʶ㷺
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ӰǵճΪĴҶȤĻ⡣Ȼڵʱ
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ԭù¡

ڹ۲ݵĴ¼ڼ˼¼ƽֵƽֵȻ
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ļ¼кܴļֵʱƽֵ˼¼Ӱ죬 
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ƽֵȻƽֵȥƽƽֵ

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ΪҪؼ¼ԼʱӦòȡͳһ淶㲻ͬ
Դݵ໥ȽϺӡ֤Ҳڹ۲֮ĽЩҪ
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һ׾ǽʾ˳лԳӰ졣Ĺ۲
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۲ݶԱȲ֤ݵľȡûʼѧ1789׶ĵ
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ΪһλĿѧ̽ߣûڷ֡ȵЧӦ
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ЧӦԴǶȡůȣϿȶ
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Լ߾ȵֵģʽ֤ʵף±Ϊо
֮һҲͬܵõΪӢʼѧԱ

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ڻʱӢ׶سлӾ硣1800-1830 ˿ڴһ
ӵһʮ򡣻µĹǷӳʱڳлԳӰ졣
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Ĺ㷺ע֮йصоӣصоµָ

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Ϊһѧߣ֮ȡ׿ԽĿѧɾͣ͵ʱӢ
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Կѧİôʹڻ֧ƶĿƼչߣǶ
ѧͿлṩ˽˾顣ҪдȰѧ߽
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ʱδܹѧרҵѵҲδԼǿѧ
ҡԿѧϵİôʹѧϰµĿѧ֪ʶ˼⣬Լ
ҵҵؽгڵ۲⹤۹ڵһЩνġѧҡ
ѧ˵ѧ͸ƾҳֽ֤ųƹ񡰸°ͺղ롱ѧ
⣻͸Ʒ˱ʵ֤˵ۺѧ
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ЩѧҡΪѧġȫ
ѧʵòߣЩƵ־ͻһĻһĻͣȫݡ
ҵĿѧˮƽʹҲõߡ


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ʦӺϹĺɭҲһƪĵĵһ
ߡڶƴԭӹ׶ˡ޲ȥСԱ
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֮ǰɭľֻһԼгӵļģ͡ļ
㽫Ϊʵۣ֤ʵԺǱ192511
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ʮѦ̵ĺճ߸˺ɭ硣


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Ѧʥڼзķ֮1926䴴󱬷
ƪģ춨֮Ϊѧѧ޵
ҫԻ͵սСʻ¼ЩĽἯǰ
С

ǰţΪܹ׼ȷرѧһµѧԣ
΢֡ѧʱʼʽΪϵͳĿѧţѧ
˹Τ飬ߺɭʿоѧҵְҵ
΢ַѽѷ֡ӦѧҲ֮졣

ѩɽùѦֻ20ǰһ΢ַ̽̿顣ڹ
ϵ²ϵĲ֮һʱҲûԭ⣬Ҫ
ɽİ²ųɹ

ǷѧϣصѾ΢ַϵͳо
ճһ½̲ġѦ̵ʱ°汾ԭɽϾͿӭ
ж⡣ˣҲֻʱԼҳ˴𰸡Ͼ
΢ַѾΪǵġĸ

19263ĵһƪѦԼ̵ıʵƳĲ
̡ΪԼ¼꾡ռ෴Ŀбʼɢ£ֻ
߹·º۹ķֹ
൱򵥣ͳľ䲨һ΢ַ̡յ²ϵ
ƵʲɶܣȻٰѶܲΪ֮ͿԵõѦ
̷̵ѧʽ

뾭Ĳһ΢ַ̺Ľⶼģûзġ
ӡԾǨѦ̺ѵҳߵĶӦϵ

䲨ضı߽»פĽ⡣ϣذ
ǽ̬eigenstateһġֵeigenvalue
ǡѦ̷Ҳһı̬ǵ²פΪḻ
άռеķֲЩֲ̬üڲĸͬ
ܼҲȻͬıֵѾϤ

ھĲУƵĲ֮ĸû
һµƵʣƵbeatƵƵ֮˲
ԾǨϵǲԾǨ߱޷˲ʱ
ѣ뾭Ȼ̡

Ѧ̵·ͬʱΪĹ͵²פṩ˼ʵ
ѧȲҪЩеĹҲɭΪع
첻ıӵĲԱֵ̬ķʽķȻ
ӿ֣κע롣


Ϊÿɹ۲Ĺײԭģͣɭڲ֪·˾
ѧһµԣֿͬڡѶֻ
þ򵥵ԭӣ˶δ

ѦĵĵһӦǳ档ͬѲϿΪ籾
а˵Ѧ̷̽ʿšͬʱҲɵһ
ԼʹһʱԭӡѦ̵
ǲɵľ֮͡

ȻóĽȫһ¡

ǵĵʦĩơҲڶҡĩѦ̵ʱֱ
ȫһɺԣܿĿ˵ѧȻ֣ȴڸӲ
ÿ¡Ѧ̵ĵһǣṩѧıֱ۵ͼ

ոշֵױֱӵرһѦ̷
ʱǲҪѧϰĪľѧˡ

ɭԤڵĲδžѾѦͻڡ
ĩơ̡ꡱһı


ȻɭҲڼ4õȥֽѧ
ȻѧĩƵĽڡĸ͢Ͳĸ籾
ɵġǡɭĻڰ֡Ľ̨
һξİ˹̹ʿˡ˹ءͶ򡪡λŵ
ߡе鵽ԼӢС

ݽʮ˳˹̹ؼ͡һ߹
ֵĴʱ˹̹Ƶѯʺɭѧҵ൱Ǣ

ڰ˹̹ĹԢ֮󣬰˹̹ͻȻʣľ
ӵĹڣ

ɭڵȴһʱ̡гؽͣǵģûʵʵع
ӵĹ˶˹̹Ȼ·ֱ˵ʵ
ѧֻܴڿԹ۲𣿡ɭӵò졣
طʣѵǲ㴴ʱĻ˼𣿡

˹̹һЦԻҲǰɡͬһЦǲظ
ġ

ɭΪ˹̹ͬ߼ʵ֤ľѧ֪
˹̹ǰӲϤ·ʱһֱֻ̬ȡڸ׷
˹صбʾɭһӴѼ͢Щ
ȴš

ں󣬰ֵʦüһãһȡ˹ھ󡢲
չı档ۻİ˹̹е㷳ܽ᣺һֱûо
ȷѧͻȻ֮Ƕͬۻݡ
ǶԵģҲûһȷġ

ϣ䣬ϯеĸǣWalter Gordonվ棺մ
ʿ˵Ѿ֤ʵͬһ


ʰʱɭһѡ

Ѿ׼ٶȥ󣬵βֲͬʱڸ籾ѧ
ʦѧȴͻȻƸ顣25ܹڵ¹
δţһѵõĻᡣɭеȡᣬѯʰ˹̹


Ϊÿѧİ˹̹˼ػشȥɰɣ
㲻ڵġźɭһȽȽǣԺ󲻻ȱ
Ļᡣɭ˰˹̹Ľ顣

ѦҲæĴѧ7£Ľڡ¹ѧĵطֻ
ǡҲۻᡣѾڸ籾ְĺɭϻμӡѦ̵Ľ
ӵڡʱŵĺɭ̲סʣ
ܽ͹ЧӦնɢ䣿

ʱĺɭѾ˲ʿѧλǰʲǸѧ
Ͼֻ֡ʦʿѧڲ˼ȻԺɭ
ߵά޿̣վʹ⺣ɭûò

άҲѦ̵ѡѦ̻ڻѩӪĥķʱһֱ
άͨűչʱάʮҲԽ޴ҵȫӹɣ
Ѧ̽ڿ϶ܿҳ취ġתͷҸ溣ɭˣҪ
ҲҪĪԾǨˡ

Ȩǰɭ޼ƿʩڳĩҲûгֱ绤úɭ
Ϊʧ䡣ֻøдŸһ״ĺ󣬼̷Ѧ̵籾
һ


Ժɭ˵ѦһвⲢΪķͷ
ѧԶԶľʵáɭɻĻѦ
ϵķ

簮˹̹ǣͬʱðѧ˴ˮݡ
µȼѧ벨֮־õִɭڵʴҪ
Ѧ̵ȷû͹ЧӦͿնɢ䣬ΪǺȷΪڰ
˹̹Թӳɹ͹ЧӦķ֮һ֮Ѧ̵ĵǲȴ
صȥĸޡ

ɭľӵ˶ǷӻܼѦ
ķȴֻĲΪֵֻܼ֮ѧϵɺϡɭ
ֿɹ۲Ѧȴ֮ŵ²һš
޷͵Ĳ

ںɭһȫû塣Ѧ򷴴༥ָ
ޣ̼߱˵ֱͼ

һֵ벨ͬ˫ͣ˼棬
Զ˾ȷ걸ѧߡΪòƲķṩһʵ
Ŀɱԡ

˹̹ûϵԭԵֻ֮ڡ
ѧ֤˾Ͳѧʵȫȼֱۣ˴ˡ
෢һֻڿͷ˽дʽ
Ѧ̼ͬʱԼ֤ƪģںɭ
--ԼԼѧ֮Ĺϵ֤˶ߵϸȼۡ

ӺǾȻͬѼѧ;ͬ顣


192512£뺣ɭԼĺȥ
ΪµĽѧʡڼ䣬оþѧӵ
ײ̡ȻۺѧףҲûȡýչص¹Ѧ
̵ļΪ𾪣ȷǸΪԽѧߡײʵ
Уʶǲĸؽ壺ʲôڲ

ѧϤֲͬĲһճˮ
ýˮС߶Эһµڴ߶γɲ
ķȱǷ񶯵ǿȡһǵŲ̫˹̹
֮󣬵Ųûý飬ǵų񵴡ŲķӦų
ǿȡ

²ûȷ˵ǰӵĲʲôӦأѦ̸ɴ
ıֱӳwave function
ʲô

ѦԼ޻ɡ϶ʵʵڵģΪӻκ
ṩһֱͼǲֻڿռһصӣ
ɶͬʱһΧǵĿռֲ

Ϊ˻ӦɭʣѦͼѲķֲƵ÷ǳխ
ӡĲھҲ֤wave packet
ӣsolitonΣӷ뾭䲨һ
ԵĲȶʱܿɢΪķֲȻӲûбֳ
Ϊ

ӵĹŲɡڸ͢칫ҵĸڣΪ̽⵽ˮ
ԭոջŵĸÿ춼ʵæĸ
ڲϵУÿ춼ζһӵĵִڼʲô
ķֲ

ͨײ㣬ؿѦ̵ʲ޷Բ˵
һϰʱӦĲˮʯͷһʯͷΧ
ӿܹǸһӲءɢ
ȷű볹ѦΪͼֻЧѧʽ

밮˹̹ƵͨУϤġ
Ϊ˸Ӹ貨ʣ˹̹ΪӵĹһ
ĵ˶ڿռĳصֵļȡڹڸõǿȡ

ʶѦ̵Ĳʵǰ˹̹ĹѦΪ
ʡڿռķֲֻǱĳصֵļʡʱ
䡢صı仯Ѧ̷ʾѧɡ

ײʱӦĲͬʱ˷ɢǲӱ
ɢֻĿԡָ
ѧǲȷ֪һײĸɣֻܼ
ĳĸʡ

һʡ֡ĳصʱȻһӣ
ԱǸ׽¼Ҳ񾭵һٶײ˻ֺ
ɭǵĹЧӦͿնɢ䡣

ӵ˶ȷΪǶȡ
ʡ

1926ףڼʵĲڹͣΪѧ췭
һ껮Ͼšرָ뷨Դ԰˹̹

˹̹ȴû顣дԻѧȷۡ
иڸ⻹һȷʵĴ𰸡˵˺ܶ࣬ȴû
ǸӽǸϼһָϵۡܡΣȷšk
ӡ


ʮ˵ı任

1926ҲѧѰһꡣ

ڷеʿյӢŵһƪģ
Ϊɭľһӱӽǡ÷ǳ⣬ΪʱԼ
ɭġġδӦûûǹľ
ѧƪĵǽŵоˣһδû˵֡

ԴӲл¬ɪƸ󣬽Ųӵһѧң
ɺϿĽڡ͢͸籾׵ءɭɵһƪ
ĺŶݷʣûڽἰԼ·֡Ҳ֪
Ƿ档

˳ӢϵĺСȴʿˣڵѧ̷
Ϊһ񣬸׼Ϊ̣ǿȺֻԷ̸в
ܵĳͷܹԷỰ֮ǰ˺硢ֻĸ
һƵضڳԷ

ĵѧᷨģ˱׼븸һ
͡Ϊ˱ⷸͽҲΪ飬ڲϾڲ˵һ仰

׵רԺ˼˺Ǽг
ûпˣԼҲûѡ˵ĸ25ʱɱʱ
Ѿǽŵоҵɵǰҹ

ΪҾƶֵѧҵʱڵشѧϰʵõĹרҵ
ȻԸΥǱҵʱһսľûҵ
ֻѧУͷʼѧϰӦѧǾȷѧ
۷Ӵһ׷ѧҲֻѧȻ硣ʳ
֤۵ĺ䶯ЧӦҲע

ŬڵõرӮһѧȥŹʿѧλ

¶гĵ˲߱罻ڽţŶ
ɵͬ˵һѧϰӡÿ찴ʱ𴲣
еѧУùٳȥɢ죬͵Ĵߡ
ɴԣ˼ѧҵһ졣

ӢѧĴͳѧѧΪɵʦṩһָ㡣
ˮѧҵٳĵʦ¬ɪŮڸգRalph 
Fowler

ҲǽΨһǿչۼңںɭ
ʱ˽̸۹½չӦյҪ󣬺ɭõĵУ͸
һݡֽתĸȼеĵˣĬȴ
ѧȶΪ졣

˶˺ûúɭǸӵѧʲôʵ塣ֱʮ
һ죬ճҰⱩߡӦÿǿѧʱͻȻ
ظв۵һСΡ

ɭںʯϵȴճʱʶոշбиë
˵Ľǵ˳йءͨУӷͳ˷ǡסģ
233223Ҳ32ͳף2332
·бʱ˴˽˳ȴвͬΥ˳˷Ķ
ԡ

ֱʮֻƣֻкܲ˼ָǿܻ۵

ѧоѼ׵ĳ˷ûǸ⡣
֪Ҳǽǰľһ֪
ԼѾֺɭľѧУλ붯ľʱס
ͬ˳ĳ˻֮ʿ˳ȣ˵һв


ֻλ붯˷ķǶ׹ϵʶȴ벻
ϣĵط꣬һҹߡòװ糿ͼ
ݿţȥľѧĴͷȻҵһֽ
Poisson bracketѧ졣ʽ뺣ɭĲΪ


ţٵĶѧԡΪġͨУͨΪ֮
໥áʵһûĿջҲһŵļ
ţ֮һЩѧͼĶѧ̥ǣ֮ԸϽ
ѧŷLeonhard EulerգJoseph-Louis Lagrange
͹ܶ٣William Hamilton˳һ͵ĳŬУѧ
ڱ׸д˸ձѧʽ

µıУȡϵΪ䶯ܺ
ġ򡰹ܶѦ̹Ĳ̱˺й
ܶʽ

ǷѧҲɣSimeon Poissonϵзһ
﷽ʽԹνġ꣨canonical coordinates
ʵ뺣ɭķǶ׳˷ûйϵ

ȴؿһϵɭľѧܶʽ
ľѧû̫졣ѧеĲ¶Ϊ
˳ֵͿֱӡӻΪɭѧ

ھ֮һҲΪ
ੲȴ׽ĶӦԭṩһѧ

ķ˾ݴ˶ĲʿԼı⣺
ѧʷһѧΪĵѧλġѧʱ
δꡣ

˳Ӯòʿѧλ󣬵ֻһݽѧڸյĽ£
죬ڳΪѧʥصĸ籾͸͢ƽ


1926101գڻվӵӦõѦ̡⻹
һμ档ȴû˼ףһͷ̲סѦ̷һڵʡ

ʱԭģͽҿ۵Ļʮ֮ĵӹ
ԾǨ¸ѾɭѦ̸µ˺֧飬
ػ롰ۡȡ֮ġۡǾ󡢲Լ
ǻû˿ѧϵ

ȻѦѾ֤˾벨ѧѧϵȼۣͺɭķ粻
ûʧյɭԹź󣬲Ѧ
̸ܴɹʶʿλҲԼĽӪ

ȻѧУѧѧľȷѧţѧ˹
Τѧ˹̹ۣǶѸԵķʽɧֻҪ
Ҫķ̣֮Ҫı߽һصӭж⡣

Ѧӵ°ݵĽΪ²Ĳҵ˷ʽû
ȴ鷳ΪĲѧĪһ
ǡѧʷϵһΣϽѧԲҪ
Եġڹ͡

Ѧ̲ͬļڹֲ͡ӵʵڷֲ˶
Ĳ̶νԾǨڸ籾Ǽ
ҹҹظԱߣûû˵ءѶʡڣѦ̲Դ
𡣲ؾϣΪˮȴǹִڴͷ
һ̽ѰǣѦ̣㲻ĻΪ

ѦʱľƣȴȻִûй˳

Ϊֵĺɭǵⳡ⣬ֻڽԹۡ
¼ԲᶨѦ̵Ĳ˵üȥ΢ʡ
ʱҲѾҵһѦ̵ȴѦ̵Ĳ

Ѧ̵֮ǰãɭҲо˲̡ɹؼ
ӵĺԭӹסԲƳԭģһֱδܽ
ڲʿ޲ߵĴ⣬Ҳ۵ĵһشͻơ

ɭҲᵽʵϵľƣò
ľⷽĪ

ͬʱֺԭӵĲͬһ㡣

ѦǾֱ߱ƵͼӵĲһӵĲ
̫ǵάռķֲӵĲ޷
ɵܺͻһӵ״ͬʱĲ

ȻɭԭӵĲȴûôֱۡһά
еķֲӸԼάռ䡣Ҳ׵ؿṹ
ֱƹ㵽ӵԭӣֻǲռݵĿռά֮ࡣԭ
92ӣĲͻж276Ŀռά

ƺ˼Ѿͨ΢̵ַѧȴͻأ
աܶƹѧϵУĳѧռҵ˾ռߡ
ңѧϣҲڼͬṩӦѧߡάռ
ͱѧΪϣؿռ䡱

ȻĿռֻһѧϵıҲʾѦ
Ŀеʷֲ벣ڹ൱ģǵӸάռ
ֵļʡڶĵӸиļʷֲ뵫ȫ
ͬһѦ̷ʱ䡢ռݱ䣬伸ʼȸΪ໥
ͬ


ʱ籾סһ䣬
ÿεӰֻذʱ°ࡣϲһ˹˵յվȻ
Լѭԭ·лؼңİеҹ죬Ȼҵ
ڽⱩߡ

Ѿʶ̫оˡݳƧ
ĵΨһ޷͸Ľɫѵ˳ˡ
˶Իʱֻáǡʱ˴Ŀ˭ʹ
˵ʻ㡣һŬڲòӦһں

벣ôˡļûѧʽϲ
ľûû˵Ȧ˰Ͳƪȫѧʾˣ
ԵȾʱҲϧ̡׼ȷĴʾ
͡˲⣬Ҳֻԭⲻظһ顪Ѿ
õı﷽ʽڽųΪһλһ
ˡÿСʱ˵һʵ١

ԼеĸͿϰԵرԹ֪Ӧ
νβ˻һ䣺ǴСѧˣ㲻֪β
ͲӦüſ˵

ڲƤ£Ӳ˵ĵ˳ɼȻ

ʿжԾѧ±˽һƳһԵ
任ۣtransformation theoryΪѧṩһ
ѧ

УѧǴ̬ʸڶάϣؿռת
Ϊɡռѡȡͬ꣬ͻֲͬġ
pictureЩмѦ̵ĲҲкɭľ
۲ȼۣҶֻձı任۵ضʽ

˵һͳһѧ

ĵпָ任У
ĺгΪı󾭹һܶٱ任ȻسΪ
ı

ǣɭѦƲԭԹ۵ͻҲǹ
̡

в㣬ûܶһѧͬʱ
֡ͬѧԼҲͬݵġ


һŪУ1900Ϊ곤ɭʦСһ꣬
˺Լֶ19021926У25
µഺ¶̽ѧɾĲ껪

1925ȥѧ֮ʣԼһƪԼոɵģ
ʦĺα༭ġѧ־ְѸŽ䣬
׼;Ķֱ׷ƪĸ塣

ѧļ¡һΣǵ˶ͬ
ģԼǱĸپ߱塣

˹̹ɲɫ-˹̹ͳƺûʶͳơ
ǲɫ-˹̹ۡĲԭìܡ˹̹ͳ
ӻڵʱͬʱ۵͵̬ȴָӻݣ
ͬʱռͬһ̬

ɭڹ캤ԭӵĲʱеӻΪ
ֵıšġԳơֹӽͬһ
̬ԭƹ㣬ָӵʵ
Ȼͬࡣڲнʱı䡪ȫԳơӲɫ-
˹̹ͳƵġɫӡǵڻ
һӡǵǰڲнʱַԳơǲ
Ӳɫ-˹̹ͳƣҪһȫͬͳƹɡ

ȻΪԼȻҲûܳΪͳƹ
ɵĴʼߡ֮ǰķףEnrico Fermiͬ뷨

Ҳһ1901ˡҲǲѧ˲żü
ĸ͢Բλ࣬ˡİ׷˹˵ѧױȥ
̽˳ΪѡױȰһҪͰİ
˹غپǷġǼ밣׷˹صо飬
ģճɳΪһʦ

ܷ׵൱ֲڣûϸµطеĶԳԣ˻
ط׵ȡǵ·Ǳ-ͳơӦ
ӡ

Լʧ䡣Լרн֮Ϊͳơ


еĺɭҲԼķաڸ籾βֱ
档ʱƣȴеְ԰ѵĸ

о󣬲һҰԭ¥ԢľӸ¥е
׼䡣ԭΪֵĿͷõѦһסڵ
ɭоӰΣڡ޷ÿ찴ʱ
࣬Ϊʱİ칫һԢСʱСʱڹ
ۡǳ絽ҹͨﵩ

ŵĹУɭһԼ˼ʱ
ܹڸ籾ԭӹҲΪʱУ
ûϰࣩΪʼ޷ڰ밮˹̹һϯ̸





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