p-Adic Path Integrals for Quadratic Actions

The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude ${\mathcal{K}}_p(x^{\mathrm{\prime }\mathrm{\prime }},t^{\mathrm{\prime }\mathrm{\prime }};x^{\mathrm{\prime }},t^{\mathrm{\prime }})$ for one-dimensional systems with quadratic actions is calculated in an exact form, which is the same as that in ordinary quantum mechanics.