# Describing Electronic orbit in 3D space using A matrix.

• kenneththo85431
In summary, the author plotted out the trajectory of an imaginary electron in 3D, then represented it's points with the matrix A(x1 y1 z1). Next, he asked for pointers on where to go from here.

#### kenneththo85431

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.

Both

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?

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.

kenneththo85431 said:
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
$$M= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }$$
so that
$$M\vec{x}= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }\vec{x}=\pmatrix{\sin\left( a\right) \,y+\cos\left( a\right) \,x\cr \cos\left( a\right) \,y-\sin\left( a\right) \,x}$$
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.

kenneththo85431
Mentz114 said:
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
$$M= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }$$
so that
$$M\vec{x}= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }\vec{x}=\pmatrix{\sin\left( a\right) \,y+\cos\left( a\right) \,x\cr \cos\left( a\right) \,y-\sin\left( a\right) \,x}$$
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!

## 1. What is the A matrix used for in describing electronic orbit in 3D space?

The A matrix is used in quantum mechanics to describe the position and momentum of an electron in three-dimensional space. It represents the wave function of the electron, which is a mathematical function that describes the probability of finding the electron at a certain position in space.

## 2. How does the A matrix relate to the concept of electronic orbit?

The A matrix is used to calculate the electronic orbit of an electron in a quantum system. It contains information about the energy, position, and momentum of the electron, which are all important factors in determining the shape and location of the electronic orbit.

## 3. Can the A matrix be used for any type of electronic orbit, or only specific ones?

The A matrix can be used to describe any type of electronic orbit, as long as the orbit is in three-dimensional space. This includes orbitals such as s, p, d, and f orbitals, which are commonly seen in chemistry and physics.

## 4. How do scientists use the A matrix to study electronic orbit in 3D space?

Scientists use the A matrix to solve the Schrödinger equation, which is the fundamental equation of quantum mechanics. By solving this equation, they can determine the wave function of an electron and use it to calculate the electronic orbit in 3D space.

## 5. Are there any limitations to using the A matrix to describe electronic orbit in 3D space?

While the A matrix is a powerful tool for describing electronic orbit in 3D space, it does have some limitations. It assumes that the electron is a point particle and does not take into account the effects of relativity. It also does not account for the interactions between multiple electrons in a system.