Quantum amplitudes are explicitly constructed for /b p/-adic analogues of one-dimensional physical systems with quadratic classical actions, namely a free particle, a particle in a constant field and a harmonic oscillator.
Alacoque, C., Ruelle, P., Thiran, E., Verstegen, D., & Weyers, J. (1988). Quantum amplitudes on /b p/-adic fields. Physics Letters. Section B: Nuclear, Elementary Particle and High-Energy Physics, 211(1-2), 59-62. https://hdl.handle.net/2078.5/55253 (Original work published 1988)