Path-integral Quantum PATHTREE and PATHINT Algorithms

The author previously developed a generalization of a binomial tree algorithm, PATHTREE, to develop options pricing for multiplicative-noise models possessing quite generally time dependent and nonlinear means and variances. This code is generalized here for complex variable spaces, to produce qPATHTREE useful for quantum systems. As highlighted in this paper, a quantum version, qPATHTREE, has the ability to take into account time dependent modifications of an evolving system. qPATHTREE is shown to be useful to study some aspects of serial changes to systems. Similarly, another path-integral code, PATHINT, used for several previous systems is developed into qPATHINT. An example is given for a free particle, and it is explained why an n-tree generalization of qPATHTREE beyond the binomial tree is required for such systems, similar to code developed for qPATHINT. Potential applications in neuroscience and financial markets are discussed