82.1.波函数的统计解释 9/86 所以波函数可以写为: ok(r, t) vp(2) nr-w(k)t=pr(r) -io(k) pk(r)= (当L→∞时,相临k值及能量值趋于零,即自由粒子对应 于连续谱。) 正交归一:现在证明归一化波函数小k()构成一个正交归一函数系 (类比笛卡儿坐标系) Pi(r)yk(r)dr =(kk)=ok,k 2 L/2 L/2 42=/些a e-k少dy (k2-k2)zdz L/2 ● First●Prev●Next●Last● Go Back● Full Screen●cose●Quit• First • Prev • Next • Last • Go Back • Full Screen • Close • Quit §2.1. żêÚO)º 9/86 ¤±Å¼êŒ±µ ψk(r, t) = 1 √ V exp  i 2π L  n · r − ω(k)t  = ψk(r)e −iω(k)t ψk(r) = 1 √ V e ik·r = 1 √ V exp  i  2π L  n · r  £L → ∞ž§ƒ k Š9UþŠªu"§=gdâféA uëYÌ"¤ 8µy3y²8zżêψk(r)¤‡8¼êX £a'(k‹IX¤µ Z V ψ ∗ k (r)ψk 0(r)dτ = k   k 0  = δk,k 0 k   k 0  = 1 L3 Z L/2 −L/2 e i(k 0 x−kx)x dx Z L/2 −L/2 e i(k 0 y−ky)y dy Z L/2 −L/2 e i(k 0 z−kz)z dz