Convert from cartesian to polar coordinates

Oct 2014
7
0
Toronto
Hello Everyone,

I'm new on the site and have a question that I feel is pretty basic, but I can't seem to get it right.

I'm given a vector of the form A = (xx-yy). The mathematical paper I'm reading does a quick conversion to polar coordinates and the result is A=r(Theta), where (theta) is the unit vector in the theta direction.

I've read wikipedia's page and several links on converting between the coordinates and many of them go into the math of finding r and finding theta, but none of them show how to assign these values in unit vector notation. I don't understand why the r for the vector above ended up in the Theta direction and why the r direction is zero. Could anyone please help?

Thank you.
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey PhysicStudent.

Basically if you have unit vectors then r = 1 for that vector.

Also what are the values of scalar and vector x's and y's? If you could give some more specifics about the problem (as well as the dimension) then it would help us.
 
Oct 2014
7
0
Toronto
Hi Chiro, Thank you for replying. The example I was looking at did not have any values for x,y. It was deriving an equation and using the variables to do it. I don't know if that assumes that theta is zero. I'm aware how to find r and theta, but how to write those values out in unit vector notation is what escapes me. Basically, I'm looking how to go from

xx+yy to (?)theta+(?)r.

Thank you.
 

topsquark

Forum Staff
Jan 2006
11,602
3,457
Wellsville, NY
Hi Chiro, Thank you for replying. The example I was looking at did not have any values for x,y. It was deriving an equation and using the variables to do it. I don't know if that assumes that theta is zero. I'm aware how to find r and theta, but how to write those values out in unit vector notation is what escapes me. Basically, I'm looking how to go from

xx+yy to (?)theta+(?)r.

Thank you.
Are the x and y unit vectors in their respective directions?

-Dan
 
Oct 2014
7
0
Toronto
Hi Dan,

Yes, x and y represent the unit vectors of those directions. I'm really trying to type the unit vector notation of vectors that normally uses x, y, z with the small "hats - ^" above.

I thought this might be easier if I just provided the link to where I saw the form of the equation that is confusing me. The paper is found here:
Landau Levels paper

And the specific form of the equation is found in the last section that discusses Landau Levels Wavefunctions in Symmetric Gauge (using Polar
Coordinates). The line Use the “symmetric gauge” ... is where the equation is, with edimension used to identify the unit vectors.

Thank you for helping me with this.