例6(1)写出实物粒子德布罗意波长与粒子动能E和静止质量 的关系 1E=m1g2,解得 2 Moc Ex+moc k+meese C、E4+2E k h h my EL+2E gce (2)证明E<m12时2=b 2mo Ek ,E >>mc 2时, ≈E C 当E<<mc时,E2<<EAm1c2 hc h .入 2EKmoc 2Em Ek>>2moc2, Ek >>2Ek moc2 n hc k2 0 2 E mc m c k = − 例6 (1)写出实物粒子德布罗意波长与粒子动能Ek 和 静止质量 m0 的关系 解 2 0 2 E 2E m c hc mv h k + k = = 2 2 0 c E m c m k + = 2 0 2 0 2 2 E m c c E E m c v k k k + + = 2 0 2 2 0 1 ( ) m c c v m c Ek − − = 解得 当 时, 2 0 E m c k 2 0 2 E E m c k k (2)证明 时, 2 0 E m c k ; 2m0Ek h = k k E hc E m c , 2 0 时 2 2 0 E m c hc k = 2 0 2 2 E 2m0 c ,E 2E m c k k k Ek hc = 2E m0 h k = 8