In this paper, we study the scalar fields evolving on a FRW brane embedded in a five-dimensional de Sitter bulk. The scale function and the warp factor, solutions of the Einstein equations, are employed in the five-dimensional Gordon equation describing the massive scalar field, whose wave function depends on the cosmic time and on the extra-dimension. We point out the existence of bounded states and find a minimum value of the effective four-dimensional mass. For the test (scalar) field envelope along the extra-dimension, we derive the corresponding Schrödinger-like equation which is formally that for the Pöschl-Teller potential. Accordingly, we have obtained the quantization law for the mass parameter of the tested scalar field.