《守恒量的适用范围超越运动方程式》由会员分享，可在线阅读，更多相关《守恒量的适用范围超越运动方程式（87页珍藏版）》请在金锄头文库上搜索。
1、能量,守恆量的適用範圍超越運動方程式。,運動方程式不容易解，守恆量可以提供有用的有限資訊。,守恆量,運動,位置,物體在某位置上是存在某種潛在能力可以轉化為運動,Ui,Uf,Kf,Ki,自由拋體,彈簧,守恆量,有外力：,功等於動能變化，功與動能原理,研究,的變化,W,功造成動能的變化,定積分是曲線下的面積,x,如果外力只與位置有關,考慮一維運動,a,b,c,不定積分,函數運算,微積分基本定理,微分與積分是反運算,x,x+x,微積分基本定理的應用,假設,稱為反微分,也是一反微分,常數c可以由函數H 求出：,x,如果外力只與位置有關,一維運動的位能,x,xi,xf,是守恆量,位能 Potential
2、 Energy,Wapp,Ui,Uf,Kf,Ki,將粒子與施力者視為一個系統,再施一反向外加力 抵消該內力,使運動前後動能不變,所作的功 並未變成動能，,運動前後粒子位置改變，故定義一與位置有關的能量：,位能 Potential Energy,因此一定有一新的能量形式,mgy 有如動能一樣，定為位能,W,Ui,Uf,W,Ui,Uf,Kf,Ki,推廣後的功與動能原理,如無外力：,Ui,Uf,Kf,Ki,機械能守恆,如無外力：,Ui,Uf,Kf,Ki,位能轉化為動能,W,Ui,Uf,所以具有Potential,物體在較高位置上是存在某種潛在能力可以轉化為運動,位能 Potential Energy
3、,選擇 c,此定義只定了位能差,取,彈力位能 Elastic Potential Energy,守恆量,由位能求力,自由態：機械能大於無限遠處的位能,動能就是兩線的間隔,平衡點 Equilibrium Point,束縛態：機械能小於無限遠處的位能,在平衡點附近不遠處震盪的束縛態，他所感覺的位能近似於一拋物線，因此近似於一個以平衡點為中心的簡諧運動！,在平衡點附近不遠處，力的曲線近似於平衡點處的切線,束縛態,r,兩個粒子會不會形成束縛態？,關鍵在形成吸引位能的機制,束縛能,原子力束縛態,+ + +,+ + +,- - -,- - -,感應形成電荷分布不均,電偶極,原子力,束縛能只有約0.001e
4、V，而室溫時熱擾動能量kT0.02eV，束縛態會被破壞。,態離子束縛,+,-,-,Na,Cl,r,需能5.1eV,釋能3.8eV,若束縛可釋得1.3eV以上能量，則束縛態能量較低,離子束縛態,所加能量,束縛能3.6eV已大於室溫的熱擾動能量，故為穩定的束縛態。,共價鍵束縛態,-,H+,R,H+,-,H+,H+,-,-,電子共享使能量降低，因此形成束縛態。,共價鍵束縛態,-,H+,H+,-,解兩個原子核外的電子能量本徵態的波函數,分子能態的能階與距離R的關係？,氫原子能階,S能態,S能態機率分布,r,S能態波函數,P,P能態機率分布,s,pz,py,px,分子軌道能態,r,H+,H+,分子軌道與
5、個別原子軌道或其組合近似，當距離 r 很遠時,H+,分子軌道能態,r,H+,H+,?,電子能態波函數的機率分布在兩原子核互換下不變: 因此波函數在互換下必須不變（對稱）， 或是乘上(-1) 反對稱：,互換,因此能態波函數不能近似單純的 而是近似於兩者的組合：,在互換下：,氫分子由兩個氫原子組成，分子的電子軌道近似地可以由個別原子的電子軌道合成。,對稱 S,反對稱 A,共價鍵：分享電子所形成的吸引鍵,H2 = H-H, H:H,此兩本徵態的本徴值不同：,對稱 S,反對稱 A,分子軌道 Molecule Orbits bond,S態電子有較大機率存在於兩原子核之間，距兩代正電原子核較近，能量因此較
6、小！,對稱 S Bonding,反對稱 Anti-Bonding,分子軌道 Molecule Orbits bond and bond,S Bonding,S Bonding,A Anti-Bonding,A Anti-Bonding,bond,bond,SP3,CH4,Hybridization,SP2,位能 Potential Energy,選擇 c,此定義只定了位能差,3D空間的功,沿某一路徑,有外力：,功等於動能變化，功與動能原理,研究,的變化,W,功造成動能的變化,3D空間的功與動能,正向力不作功,3D空間的位能,沿某一路徑,位能存在的條件,保守力,若是位能定義要唯一,對任意兩路徑,
7、保守力才能定義位能！,電位能 Electric Potential Energy,靜電力是不是保守力？,垂直於 r 的運動不作功,先考慮一固定電荷Q旁一可運動的小電荷q,與A、B的方向無關,A,靜電力為保守力，可以定義電位能,萬有引力也是保守力,電位能,摩擦力是否是保守力？,回到原位,摩擦力不是保守力,動摩擦力大小是常數，但方向與速度有關,摩擦力不是保守力,W,Ui,Uf,Kf,Ki,推廣後的功與動能原理,將摩擦力視為外力Fapp,但！實驗發現,有摩擦，似乎機械能就不守恒！,內能,如果將溫度考慮進來，摩擦作的功，也能如位能，寫成一個物理量在前後狀態的改變！,Ui,Uf,Kf,Ki,Eint i
8、,Eint f,機械能如果被擴展到包括內能，能量還是會守恆！,電磁波帶走的能量,電磁能,質能守恆,?神秘的微中子 Neutrino ,COSMIC GALL- John Updike,Neutrinos, they are very small. They have no charge and have no mass And do not interact at all. The earth is just a silly ball To them, through which they simply pass, Like dustmaids through a drafty hall Or
9、 photons through a sheet of glass. They snub the most exquisite gas, Ignore the most substantial wall, Cold-shoulder steel and sounding brass, Insult the stallion in his stall, And scorning barriers of class, Infiltrate you and me! Like tall And painless guillotines, they fall Down through our heads
10、 into the grass. At night, they enter at Nepal And pierce the lover and his lass From underneath the bed - you call It wonderful; I call it crass.,衰變,W. Pauli,N. Bohr,Paulis letter of the 4th of December 1930 Dear Radioactive Ladies and Gentlemen, because of the continuous beta spectrum, I have hit
11、upon a desperate remedy to save the law of conservation of energy. Namely, the possibility that there could exist in the nuclei electrically neutral particles, that I wish to call neutrons, which have spin 1/2 and obey the exclusion principle The continuous beta spectrum would then become understand
12、able by the assumption that in beta decay a neutron is emitted in addition to the electron such that the sum of the energies of the neutron and the electron is constant. I agree that my remedy could seem incredible because one should have seen those neutrons very earlier if they really exist. But on
13、ly the one who dare can win and the difficult situation, due to the continuous structure of the beta spectrum, is lighted by a remark of my honoured predecessor, Mr Debye, who told me recently in Bruxelles: “Oh, Its well better not to think to this at all, like new taxes“. From now on, every solutio
14、n to the issue must be discussed. Thus, dear radioactive people, look and judge. Unfortunately, I cannot appear in Tubingen personally since I am indispensable here in Zurich because of a ball on the night of 6/7 December. With my best regards to you, and also to Mr Back. Your humble servant W. Pauli,Cowan and Reines 1955,Cowan and Reines 1955,Homestake,Kamilkande 日本神岡,
