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QUESTION-2 : The transformations from cartesian coordinates (x, y, z) to parabolic coordinates (u, v, ( ) are given as in the following: x= Ju v Coso y= vu v Sing 1 2 z= - (u - V) . a- Find the Laplacian operator is given V2 - 4 a 1 utv Qu in parabolic coordinates. b- By separation of variables method, all three parts of Schroedinger equation (m=1, h =1) in parabolic coordinates (for example, for an atom in an external electric field) V 2 4 + 2 E +- 4=0 1 + v r = V 2 (UE [0, co) , VE [0, 0) and ( E [0, 27) ) . Solve the u dependent part of differential equation (E