If is a connected hypersurface of closed dividing the sphere into two connected components, and if is a function on the ambient sphere whose restriction to is then:
for points where is the unit normal on . See Pliakis 2014.
Now let’s try to understand what the Schroedinger equation:
can mean slowly and carefully. Let’s totally open up our imagination to consider the possibility that this potential is exactly something like $(N^2 + d H)$ because that is very interesting.