1、 科目:近代物理 編著:秦立原 本power point教學檔案內容，乃教師本人根據 Arthur Beiser之Concepts of modern Physics原著演繹並解讀而成。請尊重智財權，勿任意下載流通。Modern Physics Special relativity Particle characteristics of wave Special RelativitySec.1.1:All motion is relative;the speed of light in free space is the same for all observers.remark:(1)The
2、 above two statements have no dependence,the first is not the cause of the second and the second is not the cause of the first.(2)All motion is relative means that,when we say something A is in motion,the motion must relative to something B).And B is also in motion to A,this is just the thing the fi
3、rst statement want to express.(3)Observers in the second statement represents inertial frames of reference.An inertial frame of reference is one which Newtons first law of motion holds.Any frame of reference that moves at constant velocity relative to an inertial frame is itself an inertial frame(4)
4、The word free space in the second statement is very important.The speed of light in free space is 2.998108m/s for all inertial frames of reference.Postulates of Special RelativityPostulate 1:The laws of physics are the same in all inertial frames of reference.Remark:So called the laws of physics inc
5、ludes:(p15.,Eisberg)(1)Electromagnetic phenomena(including the fact that the propagation velocity of light is equal to the constant value c)(2)The laws of mechanics:Fig.1.6 discuss this postulate.In that fig.,the speed of a spacecraft relative the earth is assumed to be v and v is greater than c(lig
6、ht speed in free space).A man in the spacecraft switches on a flashlight to the front of the spacecraft and he would see the flashlight illuminates the front wall of the craft.However,the observer on the earth would see the flashlightilluminates the back wall of the craft,because vc in theearth fram
7、e of reference.Now,the flashlight is seen to illuminates different parts of the craft bydifferent frames.It is just the different results which conflict with the postulate one.So we know the assumption that v,the speed of any spacecraft must not greater than the constant c.And we can conclude that t
8、he speed of nothing can greater than the constant cPostulate 2:The speed of light in free spacehas the same valuein all inertial frames of reference.Unlike postulate 1which is based on pure thinking and life experience,postulate 2 is based on the resultes of many experiments.Fig1.1illustrates postul
9、ate 2.Jack is in the earth,Lee in a spacecraft.When the craft pass him with v=(2/3)c,Jack turn on a searchinhlight.Jack will surely find the speed of the searchinglight is c.However,Lee will find the speed of the searchinglight is also c,but not(1-2/3)c.Particle properties of wavesIn classical physi
10、cs,particles and waves are separate components of physical reality.The mechanics of particles and the optics of waves are traditionally independent disciplines.They both have thtir own serious experiments and principles correspond those experiments.However,we find that a moving particle,such as an e
11、lectron,can be seen as a wave.Simiarly,under some cases,electromagnetic waves behave as if they consists of streams of particles.Then we can see an EM wave as a particle.Together with special relativity,the wave-particle duality is the central of modern physics.In 1864,Maxwell suggested that acceler
12、ated charges generate linked electric and magnetic disturbances that can travel infinitely through space.If the above mentioned charges oscillate periodically,disturbnaces will becomes waves,and E,B,v will prependicular to each other,where v is the propergation velocity vector of EM waves.Before the
13、 suggestion was proposed by Maxwll,people only knew the Faradys induction law:A changing magnetic field can induce a current in a wire loop.Maxwell proposed the converse:a changing electric field has a changing magnetic field associated with it.The product of electric permittivity and magnetic perme
14、ability is derived to be equal to the inverse of c2,it cant be just an accident.So Maxwell again suggested that light consists of EM waves.During Maxwells lifetime,No experiments found the existence of EM waves.In 1888,Heinrich Hertzs experiment showed the existence of EM waves.He found the EM waves
15、 could be reflected,refracted,and diffracted.Blackbody radiationsWhen discussing blackbody radiations,radiations are not reflections.They are the nature ability of matters,the higher the surrounding temperature is,the stronger the radiations are.Why did scientist be interested in blackbody?The answe
16、r is the reflection ratios of different matters are also different.It effects the detecting of radiations.If scientist could exclude the existence of reflections,they would be able to see all the collected light as pure radiations without any reflections.So that scientist can concentrate their atten
17、tion on the relation between the intensity of radiations and temperature.The ability of a body to radiate is proportional to its ability to absorb radiation.In blackbody spectra.The spectral distribution of energy in the radiation depends only on the temperature.The higher the temperature,the greate
18、r the amount of radiation and the higher the frequency at which the maximum emission occurs.Rayleigh and Jeans considered the radiation inside a cavity of absolute temperature T whose walls are perfect reflectors to be a series of standing em waves.They also combined the formulas of the standing wav
19、es density and classical average energy per standing wave.So Rayleigh and Jeans derived(2.3)Planks treatment for blackbody radiationIn the cavity of blackbody model,each standing wave represents an EM waveand emitted from an oscillator.The energy of each oscillator is.In the cavity,the value of is n
20、ot uniq,just asnnh the case of the standing wave generatedfrom a vibrating string,whose length=L and two ensd is fixed.The focus of Planks treatment is not the distribution of,because()hasbeen derived to bevG v dv23 8/.The focus of Planks treatment is the distribution of,consequentlythe distribution
21、 of.The weight of is exp(/)for a fixed.So the the avergy energy of an oscillator innnv dv cnhvnkTvs exp(/)/exp(/)exp(/)/exp(/)=/exp(/)1(2.6)nnnnkTkTnhvnhv kTnhv kThvhv kT(2.6)is also the average energy of the standing waves with the fixed frequency in the cavity.For those standing waves with greater
22、 .This average energy will be smaller so that cancel the effect of G()for the greater .Example(2.1)talk about the evidence of quantum effect.The energy of a quantum,h,is 10-29 times of n h ,0.04J,the total energy of the fork.10-29 times is so small that we say the evidence of the quantum effect is v
23、ery small(But we cant say there is no quantum effect).If we want to increase the evidence of quantum effect,we should decrease the value of n very rapidly.If its value(1029)can be decreased to smaller than 10,we should be able to say the quantum effect is evident.But the strike force to the fork can
24、not be decreased to so small a value (Remember that the value of the fork is 0.04J,Its uneasy to make it become 0.04 10-28 0.04 10-29)例(3.1a)中golf ball 非oscillator，故欲論其能量量化明顯與否時，必須先令其能量可以量化。故須令golf ball 侷限於箱中運動。而此例中ball 活動空間並未受 侷限，故只能討論其波動行為之明顯性。此例中之golf ball 雖波長太小而不易發現其波動行為；但因與例b中 之electron均具明確之波長故
25、=0,s.t.p=0，使x=(由測不準原理)。故在運動方向上各處均可出 現，而並未被侷限住(例3.5中之marble就被侷限住了，故p0，s.t.0且能量被量化)原子核的尺寸 最靠近的距離Chin:(1)此值係指動能全耗盡而變為電位能時之距離 (2)拉塞福之理論用至 推導Au原子核之尺寸,其值雖為 實際值之五倍但於數量級上之評估已堪稱卓越也原子的行星模型及其為何失敗電子速度氫原子的總能量原子中的電子波動軌道上的電子波長軌道穩定條件波耳原子的軌道半徑波耳半徑1,2,3,n2nnr11015.29210 mar 對應原理 量子數越大時，量子物理越接近古典物理。一個繞行圓形軌道的電子所輻射出來的電磁
26、波頻率會等於旋轉的頻率和旋轉頻率之諧波頻率（也就是旋轉頻率的整數倍）。旋轉頻率 光子頻率 軌道穩定的條件2nhm r 量子力學 Quantum MechanicsChin:粒子存在整個空間中之總機率為1，此可將波函數予以正規化。Chin:波函數絕對值之平方為機率密度而不為機率。5.2 波動方程式 The Wave Equation()it xyAe222221yyxtxyF t波動方程式可有許多種類的解，包含了複數型式。波動方程式偏微分cossinxxyAtiAt5.3 薛丁格方程式：時間相依型Schrdingers Equation:Time-Dependent Form2(,)2pEU x
27、 tm一維的時間相依型薛丁格方程式如下:-15(1)=500,()_(b)(:4.136 10)pckeVkeV cheV s-12寫出計算過程並將答案填入空格中已知粒子之靜止能量及其值均求 a)此粒子之波長=_ 10m此粒子之動能=_此粒子之相速度=_c(d)此粒子之群速 度=_c(2)某粒子被限於x=0至x=L之無限堅硬一維箱中,(a)x=L處,此粒子之之波 函數為 提示 (b)n2=sinn=1_(c)=_,n xLL則對之狀況而言,粒子出現在處之機率最大,前述之機率最大值(3)設一限制於x軸上之粒子,在x=0與x=1之間的波函數為=ax;而在其他位置 則為=0.(a)求此粒子在x=0至x=0.5間出現的 機率=_?(b)求粒子位置之期望值=_(4)物質波之雙狹縫繞射實驗中若將狹縫1,2分別打開所得波函數分x=12,別為密度=及則將兩狹縫同時打開時,螢幕上之機率 _近代物理期末考題及題解(1之c,d)
