For the Helmholtz differential equation to be separable in a coordinate system, the scale factors in the Laplacian
(1)
|
and the functions and defined by
(2)
|
must be of the form of a Stäckel determinant
(3)
|
For the Helmholtz differential equation to be separable in a coordinate system, the scale factors in the Laplacian
(1)
|
and the functions and defined by
(2)
|
must be of the form of a Stäckel determinant
(3)
|
Weisstein, Eric W. "Robertson Condition." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RobertsonCondition.html