Math 402 Set VI1.Convert [²ψ(x,y,z) - λψ(x,y,z) = 0 ] to a "covariant" form which transforms like a tensor under a generalizedcoordinate transformation, dxi= Aijdqj. λis a scalar ( a numerical constant and independent of the coordinate system). What is the rank of the tensor and how could you show it transforms accordingly? 2.Find the number of independent components of the fourth rank tensor, Mijm, which is antisymmetric with respect ofthe interchange of any two indices. The indices run from 1 to 3. 3.In the qicoordinate system related to the xjsystem by dxj= Ajkdqk:T'm= R'm- D'm,where T'm, R'mand D'mare tensors under A. Show that in the xjsystem: Tm= Rm- Dm.4. Use summation notation to evaluate the following expressions. Put the answer in the simplest form. The operatoracts on all functions (of x,y,z) to the right of it. Bold face typeindicates vector; ais a constant vector.a) [(1/r) x a] · r² where ais a constant vector.
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