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1、Nankai University? ? ?8ml 2h2 E1=E2= 4E1E3= 9E1E4= 16E1n = 1n = 2n = 3n = 4-+l0l0|? (x)|2? (x)xx?VA?VAX?0.0731nm0.0709nm?X?0.0731nm0.0709nm?X?0.0731nm0.0709nm?X?0.0731nm0.0709nm?Nankai University?1.1 ?(The Old Quantum Theory)1.1.1 ?(Classical Mechanics) ? “?”? ? ?(Newton)? ? ?(Maxwell)? ? ?(Boltzman
2、n ? |? ?(x,y,z)|2? |? ?(x,y,z)|2?t ?(x,y,z)?Nankai University1.2.3 ?(?The Uncertainty Principle)1927?(Werner Heisenberg)? ? ? ? ? ? ?2?xpx? ? ? ? ?2?tENankai UniversityOP?AP = OC = ?/2sin?=OC/AO=?/?x?px= psin?= p?/?x?x?px= p?= hhpxx? ipxxpxx? ?x?px?/2? iEttE?E?t ? ?/2? ? ?x p?pxOPAxy?OACNankai Unive
3、rsity?0.01kg?1000ms-1? ? ?1%? ? ?9.1? ?10-31kg? ? ? ? ?mmskgsJ mhxx33 134 1062. 61001. 01062. 6? ? ?mmskgsJ mhxx5 13134 103 . 710101 . 91062. 6? ? ?Nankai University? ? ? ? ? ? ? ? ?Nankai University?1.3 ?(State Fuction and Shrdinger Equation)W. HeisenbergE. SchrdingerP. Dirac?1932 ?Nobel?1933?Nobel
4、?Nankai University? ? ? ? ? ? ?(? Postulate)? ? ? ? ?“?”? ? ? ? ?(Quantum Mechanics)Nankai University1.3.1 ? I (Postulate 1)1. ?I. ? ? ?(q, t)? ?(q, t)?q1, q2, , qf ?t ? f = 3N?N? ? ?(state function or wave function)?|? ?(x, y, z, t)|2d? ?t?(x, y, z) ?d? ?(d? ?= dxdydz)?t? ? ?x?x+dx?y?y+dy?z?z+dz?|?
5、 ?(x, y, z, t)|2? t ?(x, y, z)? ? ?Nankai UniversityC?(?)? ? C? ? ? ?(time-independent)? ? ? ? ? ? ? ? ?(x, y, z)? d? ?( , )( )iEtq teq?Nankai University2. ? ? ? ? ?(single-valued)?|? ?|2? ? ? ? ? ? ?(continuous)? ? ? ? ? ? ? ? ?(quadratically integrable)? ? ?|? ?|2d? ?d? ? ?1(?)? ? ?, ? ? (well-beh
6、aved function) ?d2Nankai University?x?x?x?x?x?x?x?x8(c)?(d)?(a)?(b)?Nankai University?1? ? ? ? ? ? ?k1?(normalization factor) ?12*?ddKdd?2*?K1?11*?dKdNankai University1.3.2 ? II (Postulate 2)1. ?II ?m?E? ? ?(?)?(Schrdinger)?222222 2 zyx? = h/2? ? ? ? ? (Hamilton),(),(822222222 zyxEzyxVzyxmh? ? ? ? ? ? ? ?),(),(222 zyxEzyxVm? ?HE?m ? ?
