Describing Electronic orbit in 3D space using A matrix.

  • #1

Main Question or Discussion Point

I've plotted out the trajectory of an imaginary electron in 3D; next I represent it's points with the matrix A(x1 y1 z1) "throughout it's orbit":
( -1/2 -1 1
( -2 -1.5 2
(-1/2 2 3
( 1 3 1 )
2 -2 -1

Any pointers on where to go from here would be greatly appreciated. External links are helpful too.
 

Answers and Replies

  • #2
Both
 
  • #3
Nugatory
Mentor
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You'll have to tell us more. What are you trying to do here? What problem are you trying to solve? How did you come up with these four positions?
 
  • #4
Yes, I'm new to matrices and I am looking for resources to create objects in 3 dimensions then model those objects in 3 dimensions.
 
  • #5
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291
I've plotted out the trajectory of an imaginary electron in 3D; next I represent it's points with the matrix A(x1 y1 z1) "throughout it's orbit":
( -1/2 -1 1
( -2 -1.5 2
(-1/2 2 3
( 1 3 1 )
2 -2 -1

Any pointers on where to go from here would be greatly appreciated. External links are helpful too.
One way to do this is to start with a position vector in the x-y plane ##\vec{x}=(x,y)## and use a 2x2 matrix to change the position by multiplication so that ##\vec{x}_{n+1}=M\vec{x}_n##,

For instance
[tex]
M= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }
[/tex]
so that
[tex]
M\vec{x}= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }\vec{x}=\pmatrix{\sin\left( a\right) \,y+\cos\left( a\right) \,x\cr \cos\left( a\right) \,y-\sin\left( a\right) \,x}
[/tex]
If you start with position (-1,0) and choose a small ##a##, say 0.05 radians, then applying the matrix successively moves the point in a circle with radius 1 and center 0.
 
  • #6
One way to do this is to start with a position vector in the x-y plane ##\vec{x}=(x,y)## and use a 2x2 matrix to change the position by multiplication so that ##\vec{x}_{n+1}=M\vec{x}_n##,

For instance
[tex]
M= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }
[/tex]
so that
[tex]
M\vec{x}= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }\vec{x}=\pmatrix{\sin\left( a\right) \,y+\cos\left( a\right) \,x\cr \cos\left( a\right) \,y-\sin\left( a\right) \,x}
[/tex]
If you start with position (-1,0) and choose a small ##a##, say 0.05 radians, then applying the matrix successively moves the point in a circle with radius 1 and center 0.
Wow! Thank you so much!
 

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