83.1.表示力学量的算符 9/99 mym, ∑Fenn)=∑cicm(mp=∑| 角动量的算符表示:在力学中,动量为成对点O的位置矢量为 产的质点对参考点O的角动量为 产×成 所以,量子力学中角动量算符为 L=产x=-i产V. (3.1-7) 在直角坐标系中 x=yPz-2Py =i (是 L、=Dx-x2≈h(z3-x32 z =rpy-yPx y ●Fist●Prev·Next●Last● Go Back● Full Screen●cose●Quit• First • Prev • Next • Last • Go Back • Full Screen • Close • Quit §3.1. L«åÆþŽÎ 9/99 = X m cmφm, X n Fc b nφn ! = X m,n c ∗ mcnλn (φm, φn) = X n |cn| 2 λn ÄþŽÎL«µ3åÆ¥§Äþ ~p!é: O  ¥þ ~r Ÿ:éë: O Äþ ~L = ~r × ~p. ¤±§þfåÆ¥ÄþŽÎ Lb = ˆ~r × ˆ~p = −i~~r × ∇. (3.1-7) 3†‹IX¥µ Lbx = ybpz − zbpy = ~ i  y ∂ ∂z − z ∂ ∂y  Lby = zbpx − xbpz = ~ i ￾ z ∂ ∂x − x ∂ ∂z
Lbz = xbpy − ybpx = ~ i  x ∂ ∂y − y ∂ ∂x