The accurate time-independent quantum mechanical method developed by the present authors [K. Sakimoto and K. Onda, J. Chem. Phys. 100, 1171 (1994)] is applied to investigate a nonreactive vibrational transition, atom exchange reaction, and dissociation processes in a collinear H-2(+)(v(i))+He collision. The algorithm based on the three-point finite difference formula is replaced with the Numerov algorithm to improve on numerical efficiency for directly solving the Schrodinger equation represented by the hyperspherical coordinates (rho,omega). We have employed the interaction potential surface analytically fitted by Joseph and Sathyamurthy [J. Chem. Phys. 86, 704 (1987)] for this collision system. The energy dependence of the probabilities of the nonreactive vibrational transition, atom exchange reaction, and dissociation processes is investigated at the total energy from 4 to 10 eV, and the dependence of these probabilities on the initial vibrational state of the H-2(+)(v(i))(0 less than or equal to v(i)less than or equal to 17) ion is also studied to understand deeply this collision dynamics. These probabilities are undulatory as a function of the total energy, and show that the coupling among the channels defined by the reactant and product vibrational bound and continuum states is strong. The atom exchange reaction is the dominant process for v(i)less than or equal to 4, and the predominant process is dissociation of the H-2(+) for v(i)greater than or equal to 14 at the total energy investigated here. In order to clarify the sensitivity of this collision dynamics to the interaction potentials, we have investigated an effect of an additive two-body and nonadditive many-body interaction potentials on the nonreactive vibrational transition, atom exchange reaction, and dissociation processes. It is found that the collision dynamics is extremely sensitive to the short-range part of the potential energy surface.