Describing Electronic orbit in 3D space using A matrix.

  • #1
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

  • #3
Nugatory
Mentor
13,900
7,338
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
5,432
292
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.
 
  • Like
Likes kenneththo85431
  • #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!
 

Related Threads on Describing Electronic orbit in 3D space using A matrix.

Replies
1
Views
6K
Replies
2
Views
3K
Replies
15
Views
15K
Replies
4
Views
2K
Replies
3
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
11
Views
2K
Top