The Wavefunction Postulate

We have already described most of the requirements that a wavefunction must satisfy must be acceptable (i.e., single-valued, nowhere infinite, continuous, with a piecewise continuous first derivative). For bound states (i.e., states in which the particles lack the energy to achieve infinite separation classically) we require that tjr be square integrable. So far we have considered only cases where the state of the system does not vary with time. For much of quantum chemistry, these are the cases of interest, but, in general, a state may change with time, and x/r will be a function of t in order to follow the evolution of the system. 

Postulate I Any bound state of a dynamical system of n particles is described as completely as possible by an acceptable, square-integrable function - 3 , wi,t02, , dD ,t), where the q s are spatial coordinates, co s are spin coordinates, and t is the time coordinate. Jr is the probability that the space-spin coordinates lie in the volume element dx =dxidx2 -dxn) at time t, (f F is normalized. 

For example, suppose we have a two-electron system in a time-dependent state described by the wavefunction y, zi,a i,x2, yi, 2,u)2,t)- The spin coordinates ol would each be some combination of spin functions a and f. If we integrate over the spin coordinates of both electrons, we are left with a spin-free density function. Call it p(xi,yi,zi,x2,y2,Z2,t) = p vi,V2,t). We interpret p(vi,v2,t)dvidv2 as 

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