The quantum states of adsorbed hydrogen atom on Pd(1 1 0) surface are investigated in this work. From the calculated potential energy surface (PES) of hydrogen atom on Pd(1 1 0), the wave functions and eigenenergies in the ground and few excited states of protium (H) and deuterium (D) are calculated. Localized wave functions of hydrogen atom exist on pseudo-threefold and long bridge sites of Pd(1 1 0). The short bridge site is a local minimum from the result of PES, however, quantum behavior of hydrogen revealed that its vibration would allow it to hop to other pseudo-threefold site (that crosses the short bridge site) than to stay on the short bridge site. Exchange of ordering of the wave functions between H and D is attributed to the difference in their masses. The calculated eigenenergies are found to be in fair agreement with experimental data based from the identified vibrations of hydrogen with component perpendicular to the surface. The activation barriers measured from the eigenenergies are in better agreement with experimental findings in comparison to the data gathered from PES. (C) 2015 Elsevier B.V. All rights reserved.