Consider a one dimensional quantum mechanical particle described by the Schroedinger equation on a closed curve of length $2\pi$. Assume that the potential is given by the square of the curve's curvature. We show that in this case the energy of the particle can not be lower than 0.6085. We also prove that it is not lower than 1 (the conjectured optimal lower bound) for a certain class of closed curves that have an additional geometrical property
Minimizing the ground state energy of an electron in a randomly deformed lattice
Asymptotics of the ground state energy of heavy molecules in self-generated magnetic field
Ground State Energy of Dilute Bose Gas in Small Negative Potential Case
