Green function importance sampling

We describe here the simplified version of the released-node method with Green s function sampling. This version allows large step sizes without step size error, eliminates conditional sampling, and eliminates the use of a guide function. Importance sampling is incorporated by use of variable sample weighting. 

The Green function of interest in practical applications is the one corresponding to importance sampling, the similarity transform of Eq. (6.18)... 

We now argue that, for finite t, rejecting moves is the choice with the smaller time-step error when the importance-sampled Green function is employed. Sufficiently close to a node, the component of the velocity perpendicular to the node dominates all other terms in the Green function and it is illuminating to consider a free particle in one dimension subject to the boundary condition that have a node at x = 0. The exact Green function for this problem is... 

The human eye responds to electromagnetic radiation in the wavelength range from about 360 nm (violet) to 820 nm (red), with a peak sensitivity near 555 nm (green). While the detailed shape of this response curve depends on the individual person, studies on representative samples of human subjects have led to adoption of a standard function relating the perceived brightness (luminous flux) to the actual power of the spectral radiation. This function is referred to as V(X), the photopic spectral luminous efficiency function, and it plays an important role in photometry. 

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