摘要
定义了沿反应途径上的波函数,证明这些化学反应分子的波函数可以按同伦群做出分类,而化学反应的传播子K(R_2,t_2;R_1,t_1)可以作出同伦分解,文中例子说明了这种分解的物理含义。
Define the wave funtion on the reaction path σ:[0,1]→R (R is the atomic configuration space) as ψ(σ, r) (t, r) =ψ (σ(t), r), t ∈ [0, 1] (r is the electronic coordinates) It is proved that the homotopy claases {ψ[σ]} of the reaction path wavefunctions (functional of reaction pathes) (RPW) are the same as the reaction path homotopy classes, namely, if [σ_1]∩ [σ_2] =ω, then ψ[σ_1] ∩ [σ_2] = ω, here ψ_([σ]) is defined as {ψ (σ,r), σ∈[σ]} Homotopy expansion of the reaction propagator is derived K(R_2, t_2,; R_1, t_1) = ∑ ∫_0~1due^(1s[ω]) ω■Π_1(F^- (A)R_1) here Π_1(F^-(A),R_1) is the foundamental group of F^-(A). And the RPW can be written according to the initial state ψ_([σ]) = ∫dR_1∫_(0[σ])~1due^(is[σ])ψ(R_1, t_1) As an example, we have studied a moving paticale on a circle. The homotopy expanaion is K(v_, 1; v_0, 0) = ∑∫_(0[n])~1 due^(is[nσ]) (Z is the foundamental group of a circle) the integation in the summation is the contribution or the particle rotating along the circle for n times to K (v_0, 1; v_0, 0).
