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.

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.