Page 66 out of 78 total pages , Page 3 out of 7 pages in this chapter
Usage:
Description:
Given the Cartesian components, the function A1 returns a rank 1 spatial tensor or a specified irreducible spherical component of that tensor.
A1 (coord& pt) - When A1 is invoked with a coordinate in the argument it creates the standard irreducible spherical rank 1 spatial tensor1 assuming the coordinate is Cartesian.
A1 (double x, double y, double z) - When A1 is invoked with x, y, and z coordinates in the argument it creates the standard irreducible spherical rank 1 spatial tensor assuming x, y, and z form a Cartesian coordinate.
A1(coord& pt, int spin, int m) - When T1 is invoked with a coordinate and angular momentum components the function returns a complex number which is the l, m irreducible spherical component of the standard rank 1 spatial tensor.2 It assumes the input Coordinate is Cartesian.
A1(double x, double y, double z, int spin, int m) - When T1 is invoked with x, y, and z coordinates and angular momentum components the function returns a complex number which is the l, m irreducible spherical component of the standard rank 1 spatial tensor. It assumes x, y, and z form a Cartesian coordinate.
The rank 1 spatial tensor consists of three irreducible spherical components specified by Al,m where m 
[-1, 1]. All spatial tensor components are returned as complex numbers.
Return Value:
A rank 1 irreducible spherical spatial tensor.
Example(s):
#include <gamma.h>
main()
{
space_T SphT; // create a general spatial tensor called SphT.
coord pt(0.0,1.0,0.0); // create a coordinate point, unit y-vector.
SphT = A1(0.0, 0.0, 1.0); // SphT is rank 1 spatial tensor for the unit z-vector.
SphT = A1(pt); // SphT is rank 1 spatial tensor for the unit y-vector.
cout << A1(pt,1); // outputs the m=1 component of A1, here 
.
cout << A1(0.0,0.0,1.0,1); // outputs m=1 component of A1, in this case zero.
}
Mathematical Basis:
There are three irreducible spherical components of a rank 1 tensor. For a spatial rank 1 tensor these components are explicitly given by equation (9-5).
,
where 
is a vector with coordinates referenced to an arbitrary Cartesian axis system,
.
The function A1 will produce a spatial tensor with these components. Note that the input coordinates (coordinate point or x, y, z) are assumed to be Cartesian and referenced to an arbitrary axis system, i.e. the user must externally keep track of which axis system the tensor is expressed in.
See Also: SphA1, A2
Usage:
Description:
The function sphA1 returns a spherical irreducible rank 1 spatial tensor with components as given in the function argument list.
sphA1 (coord& pt) - When sphA1 is invoked with a coordinate in the argument it returns an irreducible spherical rank 1 spatial tensor3 with components equivalent to the input coordinate components.
sphA1 (complex v1, complex v0, complex vm1) - When sphA1 is invoked with v1, v0, and vm1 complex values in the argument it creates an irreducible spherical rank 1 spatial tensor with components equivalent to the input values.
The rank 1 spatial tensor consists of three irreducible spherical components specified by Al,m where m [-1, 1].
Return Value:
A rank 1 irreducible spherical spatial tensor.
Example(s):
#include <gamma.h>
main()
{
space_T SphT; // create a general spatial tensor called SphT.
coord pt(0.0, 1.0, 0.0); // create a pt, keep in mind this is used as spherical.
SphT = SphA1(0.0, 1.0, 0.0); // SphT is rank 1 spatial tensor for the unit z-vector.
SphT = SphA1(pt); // SphT is rank 1 spatial tensor for the unit z-vector.
}
Mathematical Basis:
There are three irreducible spherical components of a rank 1 tensor. For a spatial rank 1 tensor these components are given by A1,1, A1,0, and A1,-1, the three values taken from the function arguments of SphA1. Note that the input coordinates (coordinate point or plus, zero, minus) are assumed to be spherical and referenced to an arbitrary axis system, i.e. the user must externally keep track of which axes the tensor is expressed in. See equation (9-5) on page 168 for the relationship between the spherical components and the Cartesian components.
See Also: A1, A2
This function originally took a vector as well, the first three real values coinciding with x, y, and z, but this is no longer supported. It is marked for removal but may still work.2
The above footnote applies here also. Originally, l=0 was an option but this is no longer supported. It is marked for removal but may work by adding 0 as a additional final argument in the function call.3
This function originally took a vector as well, the first three real values coinciding with plus, zero, and minus, but this is no longer supported. It is marked for removal but may still work.
|
GAMMA Support Provided by the National High Magnetic Field Laboratory
© 1996 Scott A. Smith, The NHMFL, and The Florida State University. All Rights Reserved. |