Vacuum energy density and pressure inside a soft wall

In the study of quantum vacuum energy and Casimir effect, it is desirable to model conductor by a potential form [Formula: see text]. This “soft wall” was proposed so as avoid violation principle virtual work under ultraviolet regularization that occurs for standard Dirichlet wall. The formalized massless scalar field, expectation value stress tensor has been expressed in terms reduced Green function equation motion. limit interest, text], which approximates wall, closed-form expression cannot be found, piecewise approximations incorporating perturbative WKB expansions function, along with interpolating splines region where neither expansion valid, have developed. After reviewing this program, paper, we apply scheme wall text] use compute renormalized density pressure inside cavity various values conformal parameter. consistency results verified comparison their numerical counterparts verification trace anomaly conservation law. Finally, approximation reproduce quadratic previously calculated exactly but some uncertainty.