For spectrally negative Lévy processes, we find expressions of potential measures that are discounted by their joint occupation times over semi-infinite intervals (−∞,0) and (0,∞). These expressions are in terms of the associated scale functions and the inverse functions of Laplace exponents.

We adopt a new approach to find Laplace transforms of joint occupation times over disjoint intervals for spectrally negative Lévy processes. The Laplace transforms are expressed in terms of scale functions.