We construct the Feynman integrands for a class of exponentially growing time-dependent potentials as white noise functionals. We show that they solve the Schrödinger equation. The Morse potential is considered as a special case.

1. I n t roduc t i on Discrete Morse theory was developed by Forman [9, 11] as a combinatorial analog to the classical smooth Morse theory. Applications to questions in combinatorial topology and related fields are numerous: e.g., Babson et al. [3], Forman [10], Batzies and Welker [4], and Jonsson [20]. I t turns out that the topologically relevant information of a discrete Morse function f on ...

We present a computationally efficient pairwise potential for use in molecular dynamics simulations of large graphene or carbon nanotube systems, in particular, for those under mechanical deformation, and also for mixed systems including biomolecules. Based on the Morse potential, it is only slightly more complex and computationally expensive than a harmonic bond potential, allowing such large ...