Asymptotic solution of eigenvalue problems

摘要: Abstract A method is presented for the construction of asymptotic formulas large eigenvalues and corresponding eigenfunctions boundary value problems partial differential equations. It an adaptation to bounded domains previously devised deduce corrected Bohr-Sommerfeld quantum conditions. When applied reduced wave equation in various which exact solutions are known, it yields precisely forms those solutions. In addition has been arbitrary convex plane domain not known. Two types have found, called “whispering gallery” “bouncing ball” modes. Applications also made Schrodinger equation.