In this article, machine-learning methods are used to solve quantum mechanics problems. The radial basis function network in a discrete basis is used as the variational wave function for the ground state of a quantum system. Variational Monte Carlo (VMC) calculations are carried out for some simple Hamiltonians. The results are in good agreement with theoretical values. The smallest eigenvalue of a Hermitian matrix can also be acquired using VMC calculations. Results are provided to demonstrate that machine-learning techniques are capable of solving quantum mechanical problems.
We give here a review of the experiments that we performed in the last few years to conclude that mentals states follow quantum mechanics. As theoretical basis we give explanation of the contextual dependence of probabilities in the theoretical basis that was introduced by A. Khrennikov. In this case the classical formula of total probability does not hold true in quantum systems unless an interference terms is added that moves in analogy with quantum mechanics in which the formula of probability is violated inducing the well known effects of interference. All the experiments were carried out on normal subjects during perception and cognition of ambiguous figures. All they confirmed the presence of such quantum like interference also for mental states. From here our unequivocal conclusion that mental states follow quantum mechanics. A position of quantum mechanics as Giano Bifronte, the two faced God of mythology, is discussed with respect to its role in the analysis and characterization of mental entities.