讨论 若M是L的伴算符,则对于任意函数和U,也有 u Mud z (Mu)ud.T u Lud Lu)*ud. x 所以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(
讨论 若M是L的伴算符,则对于任意函数和U,也有 u Mud z (Mu)ud.T u Lud Lu)*ud. x 所以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(
举例 例13.2d2 分部积分两次即得 的伴算符就是它自身 第十三讲分离变量法总
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~ ~13.2 L = d 2 dx 2 ©ÜÈ©üg= Z b a v ∗ d 2u dx 2 dx = h v ∗u 0 − (v ∗ ) 0 u ib a + Z b a d 2 v dx 2 ∗ udx ¤±§¼êuÚv÷v h v ∗u 0 − (v ∗ ) 0u ib a = 0 § d 2 dx 2ÎÒ´§g C. S. Wu 1nù ©lCþ{o(
举例 例13.2 分部积分两次即得 "=--(y+() 所以,当函数和满足 的伴算符就是它自身 第十三讲分离变量法总
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~ ~13.2 L = d 2 dx 2 ©ÜÈ©üg= Z b a v ∗ d 2u dx 2 dx = h v ∗u 0 − (v ∗ ) 0 u ib a + Z b a d 2 v dx 2 ∗ udx ¤±§¼êuÚv÷v h v ∗u 0 − (v ∗ ) 0u ib a = 0 § d 2 dx 2ÎÒ´§g C. S. Wu 1nù ©lCþ{o(
举例 例13.2 分部积分两次即得 U d dr2 d r2 所以,当函数和满足 ”u-(o)ya=0 时 d的伴算符就是它自身 第十三讲分离变量法总
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~ ~13.2 L = d 2 dx 2 ©ÜÈ©üg= Z b a v ∗ d 2u dx 2 dx = h v ∗u 0 − (v ∗ ) 0 u ib a + Z b a d 2 v dx 2 ∗ udx ¤±§¼êuÚv÷v h v ∗u 0 − (v ∗ ) 0u ib a = 0 § d 2 dx 2ÎÒ´§g C. S. Wu 1nù ©lCþ{o(