Abstract
Using arguments by E. Krahn (1925), it is shown that the n-dimensional sphere possesses the following minimum property: among all connected regions of the given volume it yields the smallest ground eigenvalue of the Laplace operator with Dirichlet's boundary condition. This result is important in establishing an adiabatic invariant for quantum mechanical systems.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have