《量子力学》课程教学资源（PPT课件讲稿）第五章 近似方法 5.2 量子跃迁

5-2量子跃迁 ■当扰动依赖于时间时,就不是能级问题 而是能级间的变化问题或跃迁问题

5-2 量子跃迁 ◼ 当扰动依赖于时间时，就不是能级问题， 而是能级间的变化问题或跃迁问题

含时微扰 H=Ho+H(t)=Ho+aw(t) Hom)=EmIm),(m n=8mn22m m=1 ino p =HY H()=∑,cn()eln ioCm=心∑ (t) Omm=(em-En)/h Wmn()=(mwn

含时微扰 W t m W n i c c e W t t c t e n i H H m m m n m m H H H t H W t m n m n m n m n i t t m n n i t n n t m m n m n n = = −  =  =   =  = = = = + = +    − ( ) ( )/ ( ) ( ) ( ) , , 1 '( ) ( ) / 0 0 0             

微扰展开 ()=∑cm)(t) (O) dt (1) iomnt(o) dt (O+1) iOmnt(p) t

微扰展开 ( 1) ( ) (1) (0) (0) ( ) 0 ( ) ( )         n i t m n m n n i t m n m n m m m c W e c dt d i c W e c dt d i c dt d i c t c t m n m n    = = = = +   

初始条件和一级修正后波函数 O → (t=0)=k,Ek, cO k 边 o mk (z) 平(t)=|k()+∑ncm(t)|mn() m(t)=e-Em(/n m)

初始条件和一级修正后波函数 m t e m t k t c t m t W e d i c t t k c t i t m m i t m m k k m m k m m k   / (1) 0 (1) (0) ( ) ( ) ( ) ( ) ( ) ( ) 1 ( ) ( 0) , , 0,         − =  = + =   = = = =  

T时刻处态m)m≠k之几率 Pmnk(t)=ml(t)) H mk (te lOmma

T时刻处态 之几率 2 0 2 (1) 2 ' ( ) 1 ( ) ( ) ( )  = = =  t i m k m m k H e d i c t P t m t m k       m ,m  k

跃迁速率 Wmk=transition prob. per unit time dP mk dt

跃迁速率 dt dP w transition prob per unit time m k m k = =

周期微扰 H'(t)=AcoS(at +o) iot iOt i(a+omk)t iCOmk - ot +f "i(+O k icomp max innum 0=O mk 2 8.+ha. absorption mk, 8 k 力a, en ission

周期微扰 emission absorption imum i e F i e H F Fe F e H t A t m k m k m k m k m k i t m k m k i t m k m k i t i t m k m k , , , , max ( ) 1 * ( ) 1 ' ˆ ˆ cos( ) ˆ '( ) ( ) ( )                         = − = − = = + − − + + − = = + = + + − + −

吸收跃迁 iO Pmk(t) mk ica mk zt sin [)t/21 n[(-omk)/2]2 2m|A[n-(5+h)

吸收跃迁 ( ) [ ( )] 2 [( )/ 2] sin [( ) / 2] ( ) 1 1 ( ) 2 2 2 2 2 2 ( ) →   − + − − = − − =  − t F t t F t t i e F i P t m k m k m k m k m k m k i t m k m k m k m k                     

费米黄金规则 d P, 2T F mk mk 8lEm-(Ek+ha For emission 2 F E mk m S[Em-Ek-ho)

费米黄金规则 [ ( )] 2 [ ( )] 2 2 2               = − − = = − + m k E m k m k m k A m k m k m k F w For emission F dt dP w

电偶极跃迁 中=-eE·x=-D· E cos ot ex(e=1/3

电偶极跃迁 cos 1/ 3 ( , ) cos [ ( )] 2 ( ) [ ( )] 2 ( 0) ' cos 2 0 2 2 2 0 2 2 0 0  = = = − +   − + =  = = −  = −                 angle of D E x e E w D E Absorption D ex e H e eE x D E t m k m m m k m k m m               