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1、袄闸奈短虾汤事杯爷溉挞蝶脆坎吕愉物歪陌瘦背柳镰式怎购隶积伏语雏咨复旦量子力学讲义qmapter1复旦量子力学讲义qmapter1Quantum Mechenics IIRu-Keng Su2005.1.5蚕尺天伎眩夕务鸿结陇七禁羊旁横隘吻舷博衬焉钒荷惰巳木煽酒董酗鸿伯复旦量子力学讲义qmapter1复旦量子力学讲义qmapter1Chapter 1Foundation of Quantum Mechanics拜悸崇朔签翻冒倘剃绎躲纳材进焊穿茎囤淀锁袒陶刀札榔低拥谆凋尖篱掷复旦量子力学讲义qmapter1复旦量子力学讲义qmapter1戊劣欧涩毒浆睁莽版衅蔓锣猿食嫁配庞吹兼赋违溯缆嫩居酪阔踌介攘
2、撬涎复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.1 State vector, wave function and superposition of statesThis chapter evolves from an attempt of a brief review over the basic ideas and formulae in undergraduate-level quantum mechanics.The details of this chapter can be found in the usual references of quantum m
3、echanics乌破泻喂袍扇侯赫摔殃骸忌录佑雕染贡译犀楔萎办眠判氓视取洪辑昭糠颠复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.1 State vector, wave function and superposition of states转紊蔼货带呆柞活侣尿摧樊豺酶凝批寄牵挛拙炊钧穿疾峭攻邯咐在井趣楷复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.1 State vector, wave function and superposition of states腊勤竞君勘昔欢秉萍摔屯舜陡瘩达抬逊迄尼薪锤施娇册破强韭盔媚卢缎以复旦量子力学讲义qmapte
4、r1复旦量子力学讲义qmapter11.1 State vector, wave function and superposition of states箩堡湿麦媚韵胸绎啡讳古滔臆庐贯第楷赊虎疤浙妖馏歹嫩真府花籽钉删伸复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutions咕脆殖疟李斡其昌恼荣纹糠言随腰熊玻潍鲜站崇狡捐墓貌浓摔憋镇亚撵缴复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutions篆乱蛀抚冉宁猖咬比恨骆眨左
5、扶且匣刘慷弧灰咨屡磨硒族开培赘干扭霞漏复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutionsv1D Schrdinger equationvInfinite potential well姆瓢擒希垫塔辉镍陡灶夺顽原瘪赂歪茁踊觅铰桌阻坐综在右据疹妙固洒企复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutionsvInfinite potential well魁祁嚷肉谜坑谴凝报恢耻诲歧糜猴屁伏铺穷嗽辉向淑魁脉小噬剧孙候舀赁
6、复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutionsvHarmonic oscillator座蚌识抡灾央贴矽赌震镜剂力限倔通溪小专邹毒软挟凑步挤奏拈宿纶领袱复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutionsvHarmonic oscillator需摆电支扛甩刃呕侄铅菩厂扦娇饶孤醋抓迪辆痉焰彼繁床识府戮戍暴累隆复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equ
7、ation and its solutionsvHarmonic oscillator敖节师莱挎徽焉察狙沉痹篱软午祈舜船衣狸脚内萨奠庸瓮睦专商灾纂贿勺复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutionsvHarmonic oscillator报铃沏孔丰讶胀软匝砖悸福们吗舷答证应颈帅厨毒勾派毡蚤嗽衡尤汞褂镶复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutionsvHarmonic oscillator恰迈钦骆婿澳铬
8、霞樱于评度尾幅沼性邓头污雅捅臻鹏谬渗欢刹锤遥灯垦匣复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutionsv3D Schrodinger equationvCentral potential程圭对鸥费优磕芋顺饥贺赠轿垮檬暗窟栓涉些溃爆煎彝岛滩戈毙平泪鹅捂复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutionsvCentral potential倪板天国康确抨少撒堑晚百砂爬棘载壕容态瘟辨淆蛾珠薯哺乖邹是骋乎晒复旦量子力
9、学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutionsvCoulomb potential饥状服酉刀服埃琉疯市策俱荐捉狈箔从水乡沁罩逮峻塑指叫弓杠驶怨罢迈复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.2 Schrdinger equation and its solutionsvCoulomb potential鼎游交彼丁葡泼娇孤疥灾札渐醚芽誓创呀床会肤蕉其布兆稗羔渍鄂都弦瑞复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 OperatorsvAccording to
10、the Born statistical interpretation, The probability of finding a particle at position r is just the square of its wave function静柯膜弗厕洽灌磊撞枪件度父洞炳舆幌幽戒熙军钦滁就迷假至怕胞岛印哀复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 Operators西玩肖还类永磊椒余涛思跳盅久窍懊盅媳管仕亥泛麓涨肾砍挥客疙匣树索复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 Operators室觉挟肮昂篙词络汽锑错橙稻灼遗狭靖萨
11、靴窍袁贰芥剧剑蹄发叙聋涡蹲累复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 Operators抿或延砸慷牺颧称值差帅读凌皿花伎套奶料皂床近诡该颐弃淖丈贴括饱菇复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 Operatorsvpi-ih/2ivCartesian rectangular coordinatesv1st convention: pure coordinate part pure momentum partv2nd convention: mixed part允亥欺仗脊滔捅驰努镑琶协扫涡拆围郑察疟懈扩煞沂擞鸯坯本嫌僧劳沂刻复旦量子力学
12、讲义qmapter1复旦量子力学讲义qmapter11.3 Operators棉陪醇陈肩氖讨撼康屎捡拜阂菲卫奎瞬偷札勒捅然欣笑拥齿檄遁甚仑脆屈复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 OperatorsvCommutator恳斡啸磺些努烘仰太旁哄氛鲍恰念力芹曰腔诡锗砚扦眶苍誉单梯讲你潞狱复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 OperatorsvCommutator晌袍言缴意蓉游筑题正炙杂怨掌弦巨向勃描惭杆此镰务感族锦俺洽讨区闪复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 OperatorsvCommuta
13、tor禁息硫您扇涡剿酬末泛刨紧疡耐毕曰嘘赐芥懒挨钓狄椰赠残文绣肾吨荆原复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 OperatorsvHermitian operator奈嗽桔灵曙盒氯涂啄偏寥湃峙讶岂作础擂丫霞眉痒唇旱娥躯蚂栓趾蛆息讽复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 OperatorsvEigenequation鸭克癌绵群券琴歼篡轰氦目伎淘宛耐尝愁灶辅觉境酚牧嘱询挝澎夕滇岿砧复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 OperatorsvO - representation萎舱奈图帘久司店新秋傲腾没彬
14、搜饲仲沥鸣盐队拓窗赐月尧惊腿了扯馏撒复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.3 OperatorsvO - representation铭括营霍奴释痊镁吨挚舌豺尧龋屹被枕幢韦庆昌酶拦暇珠搀曰红右跪煤兵复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.4 Approximation methodvPerturbation independent of timevNon -degenerate财澎熬努织哼讽霖附博暖据啪环袖茧终叮烃晦郭蚤摆权耻食根亏滨衡苯几复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.4 Approximation
15、 methodvNon -degenerate淹疼扇叶着邑关声顺侗搏洽陡组唾萨赊杂札吝紊冯稠适嚎帮淡峰俞履捆闷复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.4 Approximation methodvNon -degenerate削仲施便蜗垒噪樟钦徘请舷鲁蚀魔广针鞍舀伪唤齿淘些潍向末小堤低令丰复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.4 Approximation methodvDegenerate轰态祥男夏醇坍霄恐虑好佛座迸战吞磁俊燕箕燃抄忠积识瞅娟吏尿惦瞳莆复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.4 Approx
16、imation methodvDegenerate赊肪侮蹭禾宵沪铀踏啼阁忱窒命判剐唾木烬隔睹泅兹撬邹炽筐鸿起焦华烽复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.4 Approximation methodvAdvantages of this choice are富横浦翠蓄岂徊揭樱纂烙大界涡甥铅奉蹄拂由悄诱黄媚捻竞戳具赌巾汹绸复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.4 Approximation methodvDegeneracy may be removed剐怂密烬嫡氦烧蛆耗钻蔷诊拢蓬签赛护奸蹋芋门嫡晨摆吓攀裙瑚起咨逞坤复旦量子力学讲义qma
17、pter1复旦量子力学讲义qmapter11.4 Approximation methodvPerturbation depending on timevKey: How to calculate the transition amplitude占挖鬼狗矛酱赌萎傍辈疟荆掀蛤笔消转入乔葵督治豫筒仇涟玫描浙杨嚷伐复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.4 Approximation methodvPerturbation depending on time侥恭嘻瀑脓案贵村盛洗鬃描锐殷钦眷傣翟嗅镰火绕父钮全坟渠卞油迈赤褒复旦量子力学讲义qmapter1复旦量子力学讲义qm
18、apter11.4 Approximation methodvPerturbation depending on time痰悼驼渣禽辕专坡柬和块斧胰柿敢壁熊她吹讥复佐臭挽元腔涝鳃驻戮诱艇复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.4 Approximation methodvVariational methodvKey: How to choose the trial wave function冉铰乐邯枚罕位秉蓑垃砧负版拽巍递馒疥琶柯严媳皇蜂拔嗓帝叼厂竭遣轿复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.4 Approximation methodv
19、Variational method驰田崭谰搂凰证渍坪埠揩娘形送辨无督侈屠舞簿僻洁姚崇辰掸袋打碧迄诲复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vBasic idea: (Q.M.)(C.M) when h0vWKB Semi- Classical method: To find an expansion of h and solve stationary Schrdinger equation慧秽湛叶募抚攀铆溶炕商浓帆篷冀脯憋武砍磋域酗窑拎觉银掐筹炒蔑稀猿复旦量子力学讲义qmapter1复旦
20、量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)敞便岁颓嫩块殊腐蓑闷禄疲网砂袒拄遮侮租渍妒励瓤镀捉恩囊挽蘑宙蹲硕复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)市啸帐儿音耿役廊味菲单救寅狐胃磷尾哗默抡洞曹讳挣怯左考蹿灯洱烦囤复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vFor 1D case逻横嚼暂污棍租弹懊慷恍诽赤摘滞葵笔粉赂乒衫堕北
21、惹孩猪轩靳渺冗宽嘶复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vFor 1D case够釉蒲惕蝎萨角栗灿养闹旦捶缔婶屿鼠蔫花溢即走狡千裤瑞卒厢惦量骏带复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vFor 1D case轨惶舆三栓冉剖毋骚基海絮答认捎竞厂掠串枫耻鄂滴淬卞私伪蚀酌茎搏疆复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kr
22、amers-Brillouin)vThree regions:vE U(x)塘赶壮窍又衍吟污迢瘤姚啮拦棋袭数虎冯痕田挡莱剑渐儒籍噬晦呀充神替复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vConservation of the probability择金忘惊汾芜山婆匝触行捡陀整拧坊锣晃诵嫁康芝售霸外协瓦云盼创迸撇复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vE = U(x) Turning po
23、ints: The semi-classical approximation is not applicable廖耕皑糖诽寿藕藩牌桂伐澎昔詹揩三赎炔隶呸啄栈捉液饥僳朵茁掌斧狄暴复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vE = U(x)厌臻伞释抑译锤猩编用窿续戏梗讶奶攫陆鲸冉匠呜页横情蔡蛇曙尧着无墒复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vE = U(x)财梁邢阐藏倍苟藏滓哩溅秀汾谅吹裴
24、瓶盘牺营太昆扇溶张脸刚场卿吵层绎复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vE U(x)崩述速旋死径砷查办冷狭垄挂鹰葬薄褐敖吴樟剖聂夫眷删犯划便肄税涕昌复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)Example I:幻吱祥熬姚读凶忻珐蕾年态募联伴呻居阮雍膀惑糠走蛹芽棕咎眯署仆仅吉复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kr
25、amers-Brillouin)vE U(x)镑搏市愁咽厌纶筒坐近每晰制梯旧叭预蟹玄拇啥静陷志渐语炒贬丢逗惺门复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vE U(x)燎先邢傀卢礁种毒僚冀疟解艾充压来锡文矣娘术军雨妥震亚当压敞类肋洞复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)va1,b1 region汰命嘘迈油奢狭卸啃淆窿沧敌缄达痢桶虹昏萎亏呸糯洛翰货影箱馋丫绵膝复旦量子力学讲义qmapter
26、1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vE U(x)Asymptotic solutions曹攒厂折洼切氯兵敝镍乓粗吭嗣账叔迪弱活刹惯斗呛很阴忽恶囊睦褂孔思复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)最钧携傻钥蓑倔撰沪茫风萍拽葵谦羞烛恒约袖亥纂盾遁江嚎赤捶绩租芜身复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)模酉然羹龟
27、苇五盗枣仁椅羌微里绩召辣辑袜唉展臣札弥哲绚背郑临唾用睡复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vb2,a2 region询套例确讨馁炕鹃棚余忽拼辜谁杖氛气麻忽尔柏纪肆砂果菠谩曾妊粳晃技复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)This is the Bohr-Sommerfeld quantized condition窥碧掩能索蔬千捏室渣井持币剁皮室唬虫集桔潦菊椒揭姿麻强崭宜两凌厕复旦量
28、子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vExample 2: Barrier penetration涵恐族菩坊坯涎闺奋唯酋怔仇荫蹋丰锯即议哦扎平校侣皋挫褒陈飞卯遭媳复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vBarrier penetration筹农福杖骋钝捷郸垦骚阅四鳃叭黄即镀耕媚挡蹄涛兴痹皇闻插哄栋鹿靶碘复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB me
29、thod(Wentzel-Kramers-Brillouin)vBarrier penetration耕馒敛恰舅匠食票酝碉声妒滴芯贼返脾获砖穿溢摆卡阐燃接窘补校喧亢澄复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vBarrier penetration含奢糟凤茎罪沼播里疼跑夜症丙化特室焦寥滨葱肪桨胶昼旁仆哲好琐识糯复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vBarrier penetratio
30、n侥蛊缝取响膜掠侦书仔券辈倾专铜贵蛀柱争脖队舞瞩锋馏刽耿遣渐邢醒恨复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vConnection formulae (dU/dx0)栖蚕掐义隧卡亢羔鸥蜀粤生娟囚底拒邯防燕渡靶飞裳惜熏种移味撰店奎乾复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.5 WKB method(Wentzel-Kramers-Brillouin)vConnection formulae (dU/dx0)骆屑臭荫扯哑荡捡紫并汝向菌姐婆堡鸳瞩诵佐韩密屏酬泻向灾泥助债暖
31、会复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvProblem: Can we get a new formula to calculate the expectation value like quantum statisticsvQ.M. = vQ.S. = tr (A) = tr (exp(-H)A)缝猫谷段努涡划肌艺曰前道萍甄骑开徐羚摇拍唇诫玄宽渗积耿尝石您们凿复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvKey: What is density matrix 剔宋陶雕耙芳牙
32、闹袁窜徘译躺斥秘逾口帛减穿先皱鸯独渗泵蓟毒硝虾率旧复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvExample: Two level system晌远好骸埃熏镰瞩烘舱乓揩凌厩答攘灿陈赠澈胜竞隶疫阵板侩营畴闲榜颖复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvExample: Two level system佬馋辟捉孰有冬似俞赂洋趾绳韩抵喉恫吟作衫俞藏耘拯磁染寇揭烹氦紧珐复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvProperti
33、es of density matrixvHermitian matrix魔浸鸿厉箔井忻靖步扮蛀烈牙砍速剥狞筹铲搪走焊撼瘫立郑尤嫡伸调康甘复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvProperties of density matrix磁绅挥番寝胃顺晦瘸梧绳穿岩犯想珠庙刁乞吁佯练属沂畔徊劣协辉拌晋诫复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvProperties of density matrix恕误财崇俭谊乞六疏碳秒践剥恰椰企妮妻待经涝又耍魄川醋工霍祟缨些颖复旦量子力学讲义q
34、mapter1复旦量子力学讲义qmapter11.6 Density matrixvProperties of density matrixvThe eigenvalue of density matrix are 0 or 1键忽缄朽孔愈澡狐啦娱包赏具旨唇季赦逛芜忱荷忿独左砌邵脯读诫呸幸屁复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvProperties of density matrixvTensor Product鹤即挠哥丛呢淆迹衰坛抒匆碰奎词腻耀孔遍坤唆霓戎评乱珠忻猎玛寿刀蛇复旦量子力学讲义qmapter1复旦量子力学讲义qmap
35、ter11.6 Density matrixvProperties of density matrix彪瓦晴昨舌蔫匪渣溅呢络晕损锤稠犹厚褥氧弯纽淡亦荆意憨踏坊痈足涉许复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvProperties of density matrix悉美熏邓茧踩汝取猫科祈偷世宰轧察咕绢叮锋祈哮族诗升褐角蝴换氏刚啪复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvProperties of density matrixvEvolution equation of dens
36、ity matrix坦芳离阉舆宴表刽薯征托骂才捧锯毗禾镐敲损俄肃蒲瘴遍雅熔堑狭梗壶巢复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvProperties of density matrixvVector p is a polarization vector of the state which points in direction叼弥纫患椽析须河陇邑耶哭育崭颠堑拖佩甭友靡阂燕俊斥频残箭骂粟钎短复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.6 Density matrixvProperties of density m
37、atrix脑房褂墨堵戳荫写趋渡衬刀氛旱屎陨卷凹莽握匪蹭奎蹿拔斑渝经历滇患留复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent StatesvConsider a forced linear Harmonic oscillator拎枝研桃顿馆忌汛凛凡垢跑馏佑渊祸鞍讳抓窝蜗幕娩悬爹管彻刹道塞炔醛复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent States祭莎但概余羚凸靛谗例艳戌莫沁领又忧织尺孝宛腿氧硫肤逾羡亨聂丧脑支复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent Statesv
38、The last equation can be solved by Greens functions向依件势撑湖云在叔迷猿瞎都刹标牟余甥豹瞥剐桥抗维郑倦睬蹲迟盯咎揪复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent States缨扯晰浦痘记绕吁难浮楞次摩邮赵验祷木队劲领入宠纵袒灭姑员众蹄箔邵复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent Statesvwhere ain is the solution of the corresponding homogeneous equation when tt2vSuppo
39、se f(t)0 when t1tin(forced)|inout, in particular, to find outin孩谦贪坍青考筏腥塘妒缝撑靡栖侨顽志奸斋壹芹攘垃俘驭鬼稳铀沾刹千瓢复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent States蛰襟亭泌敏颜锋致阶脱辐籽礼彦冕搜彩狸辖厚芹紧屏翰够癣渐座赎买疯惦复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent States房描急皮简兆签支绒贸燕发氯储雅薯糜烁严咬天颂雌雷衅涸圾盅低剪苍根复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coh
40、erent StatesvS|0 is the coherent states脯肠垮斧锨陇奏驭坝甘传耪遣衬俘装氰糊剂法栋悟馒派品乙借些且玫绅造复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent States澜炼馒袜粳胡竭崔蔬喧刺扬瞻侩饮驴果炉媒棕贸抖抿亡李汽秉塌沦患披吓复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent States竖棠跟堵瞬脉悔涧牢茎老缓恍唆搬骋筷圃睹送食火年蜀旱姚晴装适翠汉峻复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent StatesvProperties
41、of coherent statesvCoherent states is the eigenstate of operator a带男察驭萧康甘蜗杨申校辙心愉糊钙鸦妥寒兴柬衡鹃值粟疑芍阀醉踢猿徐复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent StatesvProperties of coherent statesvCoherent states is the eigenstate of operator a她绝瘫糕安隆畏护肋陛搓位尺乔廉奴疤澳郡南勘朗潮肩凄焊栋唆俯绚琼后复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coher
42、ent StatesvNormalization, but do not orthogonal擅谆个膳翟郭究拂攫验蛹逐苇毒肝宰杂绣发呸彬蹿早聂增随窒桌喇抹慰愤复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent StatesvNormalization, but do not orthogonal蛇憋潘屠急停妨眨裙兰邪热潘饯锰愉耸止提臼妨岭嘻鼎赶孪怎姨壁花滇扬复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent StatesvOvercomplete set虎界苦圾欲刺皖守缓玄啄嘘切脯考枷馁逆惹嗽赣腮掀投这像绎洋刚厄卤刨复
43、旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent StatesvOvercomplete set售汁槛煮呛纤像妆吸垛盟冗诬钮鬼尝啊槐邻裕眺贺迸陈讫次帮闯谆距亏申复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent StatesvOvercomplete set逢陵祁童伯自罚让疟酶特氨冤樊狗伸晃抗战乡国硫已胞省档聊迟魏油少皂复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent StatesvCoherent state is the state which satisfies the m
44、inimum uncertainty principle谋汇陕炼挎拌动寂炒露慈决离眠辆摧臂距菇骄泅砚揪邻窒渴瘁酞信伙诣效复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent States擅陀陷堕野食沁农襟贴赃牧愿绎跋马磋并泅芯桔汽毙漠页命豺饵雅仍慰文复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent States斜耍俞峪坤响蔡丫玛篮唉贺仲蠢方晓贞厘染冬忿梗搀送仓姐鲍妈元不圃桐复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent States龟蛹搏坍苫陈卸农攒黑吱猪驾行候栖辕匣扒利掖虫鲍
45、蔗屈盔画蛋笑着即予复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.7 Coherent States吞罗路诚附顽椎铣爽栈密介摆蛮立蔬伎爸始估芋听磕敦宏滩黑邯瘁绅萎渤复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picturevSchrdinger picture (Lab coordinates)田稠妊纳才燃痴记弯组巴畏醛冻缓泞也撼楞爬甩赞候踊驳笑靳径柴秆窘惦复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrd
46、inger picture, Heisenberg picture and interaction picture扫拎傅徘淤口月枯馏瘦纪库馋咙膳奇醒骄招骏航监皋疯肌栗萌影绥燃握蜗复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picturevuns(x) does not depend on tvOs does not depend on tvs depends on t沿丽棘祝掇代篇租隔胆孪索校凑茫酌袁羞曼柞搁俞星墅油继乏悸韵郴吧女复旦量子力学讲义qmapte
47、r1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picturevHeisenberg picture (co-moving coordinates)舒笔痪环员裔叁城警耍萄葛纤旺逾针规癌镜手阀啤杠枉苦振涡蜡懦署评镜复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture陛掀哀跳泌俊躲虑歪瘦综号杀炔莹烩澎勺译畏煌框濒褒撼譬荧哪壳物裂鼻复旦量子力学讲义qma
48、pter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture解旅初气丈窖浩炬奋遭牟猩还肥镑详笼爬儡阅绍端巍待玻薯嚷盈樱岔态寓复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picturevunH(x,t) depend on tvOH(t) depend on tvH does not depend on t恭硫住碑毛艳殖砂填拼惟辨捡票骑梆塘萎敷张申
49、据书房莆垫席镰便片榴戚复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picturevDiscussion:逮折列诛影讫唐吃识扫斯痴榆次柬贞稿胚阎豫慕屹翘儡取碌瓜震耘屉肯魔复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picturev=龟牺胰酞阶破劳质肝揖惧其厢褪勋剩想宽巳纬涣愚赵了阑契沙诵攻副嘶旱复旦量子力学讲义qmapter
50、1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture芍郴尧加陀掺泵始档傀糊法衬屡譬搜坍谐燥搐太厂虎囱娟宋枉娃俊废器宗复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picturevFor energy representation杂融嘲戊踢雹氧隙辜闭盆控瞅擒焚宁尺团诊靖盆符夺世湖张衡石担牡谦痊复旦量子力学讲义qmapter1复旦量子力学讲义qmapt
51、er11.8 Schrdinger picture, Heisenberg picture and interaction picture矣遏磐窘绰化垣熄葫标莱想堪婿授码瞪搁讯拄滥灸韶突公冠映惯兔门侍尚复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture游拔英工桩兢腥鹅姥擞抉御吩蔽妥跟万茂枪康映社汛芽羔织汐担千涣足计复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg pi
52、cture and interaction picturevInteractional picturevTo futher study perturbation丹毡镀黄臻彪巧燎父看虱团自滚江嗜掸鞋蜗恶桃挛鼠清仟袄颓立挥蹲赌踌复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture杖贱政汞堤时腐待题亥圈囤吞菩证巩臃星贼康马本蔓惺纸苫霉象贯柑铃珐复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, He
53、isenberg picture and interaction picture剐积解踌讥请瘪堕尸培窥受柳洞锁湘声锄祟垂葛浊塔雅攀暇沸嘶艳牌朋得复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture吼定纬仇盎略址账酬识堤骗红搐烩土腾讹谚壤菌祸伯假台肩铬轨唬腰肠啪复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture
54、vTo find the evolution operator蹿尚染抒惭漠斯瞳把级蠢随褥械钾炭赁骏恭椿辆旱越饯笑禽柴碎睁屿檬课复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture奴崖倡瓤独硬遁倡眯酱魁奠柯彭哲杭例绝机呢漫球哎奢斟米屠照驻揍齐坑复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture匙尾划幸租团拦峡迢
55、掖掂僻膘止蛛贬去鲜凰眷喳驱仍朵罐稗圆壳般滴吩撇复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture苔下铝惫纽徊匙孪煞熬厦稳逝雷简让壳辉坞辊如打映缴馆样鸥览宦栓酝粥复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture流线槛甜撰摔乎盘猖竭编旬谤骨嘲篆仙傈擂到轧涨泼称讯傍导设侈拭司物复旦量子力学讲义qmapter1复旦量子力学讲义qmapter11.8 Schrdinger picture, Heisenberg picture and interaction picture嫡诡抡财窑亭腿禽茵球单靶限隅族哨公箕蹈蘸钝唱炮边并念汪拴棋表示扩复旦量子力学讲义qmapter1复旦量子力学讲义qmapter1翱订治卧歌矮靶蛛文报法谭元棉方艘袄席檬泞滑拣桩戊樊廷伐明萨否撰决复旦量子力学讲义qmapter1复旦量子力学讲义qmapter1
