The Helmholtz differential equation is not separable in bispherical coordinates.
Helmholtz Differential Equation--Bispherical Coordinates
See also
Bispherical Coordinates, Helmholtz Differential Equation, Laplace's Equation--Bispherical CoordinatesExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Helmholtz Differential Equation--Bispherical Coordinates." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HelmholtzDifferentialEquationBisphericalCoordinates.html