Numerical Solution of Schrodingers Equation

As applied to the hard-sphere system, for example, the wave function satisfies 

In ordinary applications of the Monte Carlo method the boundary conditions are carefully contrived to make the environment of the sample mimic that in the interior of a macroscopic system (cf. Chapter 4, Section 4). At the same time, one of the attractive features of such calculations is that one can extract from them, along with thermodynamic averages, microscopic information on the structure of the system. The most common such data concern the details of the pair correlation function, although more complicated information is also available. Along this line, for instance. Hoover have proposed a study 

The macroscopic boundary conditions clearly make it difficult or impossible to get certain other kinds of interesting microscopic information, however. An obvious example is the structure of a surface region. It is therefore interesting to see what can be accomplished by choosing other boundary conditions for special purposes. Recently there have been some interesting ventures of this sort. By way of example, we draw attention to two current lines of investigation, one having to do with the liquid-gas interface and the other with effective interionic forces in electrolyte solutions. 

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Becke AD, Dickson RM (1990) Numerical-solution of Schrodinger equation in polyatomic molecules, J. Chem. Phys, 92 3610-3612... 

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