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V \ \ 8 G \ Þ. MA342H Homework #1 due Wednesday, Feb 10 1 Find all separable solutions u(x,y) = F(x)G(y) of the equation xu x u y = 3y2u 2 (a) Show that u x yu y. Title Closed subgrou Author scllo Created Date 9/12/19 PM.

Xn aw c l. P q R f } ¾. Physics 505 Homework No 5 Solutions S51 1 Angular momentum uncertainty relations A system is in the lmeigenstate of L2, Lz (a) Show that the expectation values.

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SOLUTIONS TO SECTION 1 5 Solution We have u x=u ss x u tt x= u s 2u t u xx=u sss x u stt x 2u sts x 2u ttt x= u ss 4u st 4u tt u xy=u sss y u stt y 2u sts y 2u ttt y= u ss 2u st u y=u ss y u tt y= u s u yy=u sss y u stt y= u ss Substituting these expressions into the given equation we nd. A @ c . Title Math 53, Discu Author Izak Created Date 4/29/ 13 PM.

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# $ % &. Exercise 61 2 Find the solutions that depend only on rof the equation u xx u yy u zz = k2u, where kis a positive constant (Hint Substitute u= v=r) 4 Solve u xx u yy u zz = 0 in the spherical shell 0 <a<r<bwith the boundary conditions u=. D q O w ³.

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Chapter 1 Partial differentiation Example 11 What is the maximal domain of the real function g defined by g(x) = √ x2 3x2?. A m e v l l ;. G b y u , , <.