Quantitative Observability for the Schrodinger Equation with the Anharmonic Oscillator |x|
Establishes an observability inequality - bounding a solution's total initial L2 energy by the energy it deposits on an observation set E over an arbitrarily short time (0,T), with an explicit constant C_obs(E,T) - for the Schrodinger evolution generated by H = -d^2/dx^2 + |x|. It gives sufficient and necessary conditions for observable sets and proves half-lines are NOT observable, a geometric departure from the |x|^{2m} (m>=1) potentials. The proof introduces a new Ingham-type spectral inequality, a quantitative unique-continuation/compactness argument in the spirit of Bourgain-Burq-Zworski, and Szego's limit theorem for Toeplitz determinants as a tool for counterexamples.
QUANTITATIVE OBSERVABILITY FOR THE SCHR ¨ODINGER EQUATION WITH AN ANHARMONIC OSCILLATOR SHANLIN
Studies observability inequalities for the free Schrodinger evolution generated by the one-dimensional anharmonic oscillator H = -d^2/dx^2 + |x|. An observability inequality bounds the total initial …