伴算符 Definition 设L和M为定义在一定函数空间内的(微分)算 符,若对于该函数空间内的任意两个函数和, 恒有 (U, Lu)=(Mu, u) 即 Lud (Mu)ud.r 则称M是L的伴算符
Eigenproblem of Sturm-Liouville Eqn Method of Separation of Variables . . . Eigenproblem of Self-Adjiont Operators Eigenproblem of Sturm-Liouville Eqn Degeneration in Eigenproblem of S-L Eqn Î Definition LÚM½Â3½¼êmS(©) ΧeéuT¼êmS?¿ü¼êuÚv§ ðk (v, Lu) = (Mv, u) = Z b a v ∗Ludx = Z b a (Mv) ∗udx K¡M´LÎ C. S. Wu 1nù ©lCþ{o(
举例 例13.1L、d d 以,当和都满足边界条 的伴算符是
Eigenproblem of Sturm-Liouville Eqn Method of Separation of Variables . . . Eigenproblem of Self-Adjiont Operators Eigenproblem of Sturm-Liouville Eqn Degeneration in Eigenproblem of S-L Eqn Þ~ ~13.1 L = d dx Z b a v ∗ du dx dx = v ∗u b a − Z b a dv ∗ dx udx ¤±§uÚvÑ÷v>.^ y(a) = y(b) § d dx δ− d dx C. S. Wu 1nù ©lCþ{o(
举例 例13.1L、d d 所以,当和都满足边界条件 时,一的伴算符是
Eigenproblem of Sturm-Liouville Eqn Method of Separation of Variables . . . Eigenproblem of Self-Adjiont Operators Eigenproblem of Sturm-Liouville Eqn Degeneration in Eigenproblem of S-L Eqn Þ~ ~13.1 L = d dx Z b a v ∗ du dx dx = v ∗u b a − Z b a dv ∗ dx udx ¤±§uÚvÑ÷v>.^ y(a) = y(b) § d dx δ− d dx C. S. Wu 1nù ©lCþ{o(
举例 例13.1L d 所以,当u和都满足边界条件 y(a)=y(b) d d 时,,的伴算符是
Eigenproblem of Sturm-Liouville Eqn Method of Separation of Variables . . . Eigenproblem of Self-Adjiont Operators Eigenproblem of Sturm-Liouville Eqn Degeneration in Eigenproblem of S-L Eqn Þ~ ~13.1 L = d dx Z b a v ∗ du dx dx = v ∗u b a − Z b a dv ∗ dx udx ¤±§uÚvÑ÷v>.^ y(a) = y(b) § d dx δ− d dx C. S. Wu 1nù ©lCþ{o(
讨论 若M是L的伴算符,则对于任意函数和,也有 vud LOud. 以L也是M的伴算符
Eigenproblem of Sturm-Liouville Eqn Method of Separation of Variables . . . Eigenproblem of Self-Adjiont Operators Eigenproblem of Sturm-Liouville Eqn Degeneration in Eigenproblem of S-L Eqn ?Ø eM´LΧKéu?¿¼êuÚv§k Z b a v ∗Mudx = Z b a (Mu) ∗ vdx ∗ = Z b a u ∗Lvdx ∗ = Z b a (Lv) ∗udx ¤±L´MÎ C. S. Wu 1nù ©lCþ{o(