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2) Rotations in 3D space, given by group SO(3), can be obtained by extending SO(2). For rotation in 3D space by angle through the z can be described by 3x3 orthogonal matrix R₂(9) = coso -sino 0 sing cosp 0 0 1 dRz Using the same procedure, find the generator S₂= −i Tp=0 do

2) Rotations in 3D space, given by group SO(3), can be obtained by extending SO(2). For rotation in 3D space by angle through the z can be described by 3x3 orthogonal matrix R₂(9) = coso -sino 0 sing cosp 0 0 1 dRz Using the same procedure, find the generator S₂= −i Tp=0 do

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Thank you, can you do this with the this problem too? 

2) Rotations in 3D space, given by group SO(3), can be obtained by extending SO(2). For rotation in 3D space by angle through the z can be described by 3x3 orthogonal matrix R₂(9) = coso -sino 0 sing cosp 0 0 1 dRz Using the same procedure, find the generator S₂= −i Tp=0 do
Transcribed Image Text:2) Rotations in 3D space, given by group SO(3), can be obtained by extending SO(2). For rotation in 3D space by angle through the z can be described by 3x3 orthogonal matrix R₂(9) = coso -sino 0 sing cosp 0 0 1 dRz Using the same procedure, find the generator S₂= −i Tp=0 do
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How about this:

SO(2) can be extended for 3D rotation through the x-axis by an angle α. 

Rx (a) = 1 0 10 0 0 cosa sina -sina cosa. dRx da Using the same procedure, find the other generator of SO(3), which is Sx= —i ·la=0
Transcribed Image Text:Rx (a) = 1 0 10 0 0 cosa sina -sina cosa. dRx da Using the same procedure, find the other generator of SO(3), which is Sx= —i ·la=0
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