举例 什么条件下|*-()yu=0?
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~ o^e h v ∗u 0 − (v ∗ ) 0u ib a = 0º ¼êuÚv÷v!!na>.^ α1y(a) + β1y 0 (a) = 0 α2y(b + β2y 0 (b) = 0 (Ù¥|α1| 2 + |β1| 2 6= 0, |α2| 2 + |β2| 2 6= 0) ¼êuÚv÷v±Ï^ y(a) = y(b) y 0 (a) = y 0 (b) C. S. Wu 1nù ©lCþ{o(
举例 什么条件下|*-()yu=0? 函数和满足一、二、三类边界条件 ay(a)+(a)=0a2(b+2(b)=0 (其中a12+12≠0,|a2+12≠0) 函数u和满足周期条件
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~ o^e h v ∗u 0 − (v ∗ ) 0u ib a = 0º ¼êuÚv÷v!!na>.^ α1y(a) + β1y 0 (a) = 0 α2y(b + β2y 0 (b) = 0 (Ù¥|α1| 2 + |β1| 2 6= 0, |α2| 2 + |β2| 2 6= 0) ¼êuÚv÷v±Ï^ y(a) = y(b) y 0 (a) = y 0 (b) C. S. Wu 1nù ©lCþ{o(
举例 什么条件下|*-()yu=0? 函数和满足一、二、三类边界条件 a1y(a)+(a)=0a2(b+2(b)=0 (其中|a12+132≠0,la2+12≠0 °函数和满足周期条件 y(a)=y(b)y(a)=y/()
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~ o^e h v ∗u 0 − (v ∗ ) 0u ib a = 0º ¼êuÚv÷v!!na>.^ α1y(a) + β1y 0 (a) = 0 α2y(b + β2y 0 (b) = 0 (Ù¥|α1| 2 + |β1| 2 6= 0, |α2| 2 + |β2| 2 6= 0) ¼êuÚv÷v±Ï^ y(a) = y(b) y 0 (a) = y 0 (b) C. S. Wu 1nù ©lCþ{o(
自伴算符 Definition 若算符L的伴算符就是它自身,即对于该函数空 间内的任意两个函数和U,恒有 (U, Lu)=(Lu, u 即 u*Ludr=/(Lu)ud 则称L是自伴算符
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 gÎ Definition eÎLÎÒ´§g §=éuT¼ê mS?¿ü¼êuÚv§ðk (v, Lu) = (Lv, u) = Z b a v ∗Ludx = Z b a (Lv) ∗udx K¡L´gÎ C. S. Wu 1nù ©lCþ{o(
举例 例13.3L、:d C. S. Wu 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~ ~13.3 L = i d dx Z b a v ∗ i du dx dx = iv ∗u b a − i Z b a dv ∗ dx udx uÚvÑ÷vÚ~13.1Ó>.^ y(a) = y(b) Z b a v ∗ i du dx dx = Z b a d(iv) dx ∗ udx ¤±i d dx ´gÎ C. S. Wu 1nù ©lCþ{o(