The program Scheme2Clebsch is written up in the language Scheme according to the formulas described above. Section snippets The method of calculationĪ common algebraic expression for the Clebsch–Gordan coefficient describing the coupling of the angular momenta j 1 and j 2 with projections m 1 and m 2, respectively, to the total angular momentum j with projection m is, = δ m 1 + m 2, m Δ ( j 1, j 2, j ) ( j 1 + m 1 ) ! ( j 1 − m 1 ) ! ( j 2 + m 2 ) ! ( j 2 − m 2 ) ! ( j + m ) ! ( j − m ) ! ( j − m ) ( 2 j + 1 ) ∑ v, where Δ ( j 1, j 2, j ) = ( j 1 + j 2 − j ) ! ( j 1 − j 2 + j ) ! ( − j 1 + j 2 + j ) ! ( j 1 + j 2 + j + 1 ) !, and the sum runs over such (integer) values of ν that no The structure of the program Scheme2Clebsch In Section 5 we show some sample results. The use of the program itself is described in Section 4. Section 3 describes the structure of the program. In Section 2 we present the expressions employed in calculating the coefficients. The program offers a platform-independent graphical user front end which allows a user-friendly calculation of the coefficients under consideration. The Scheme programming language has the built-in functions for operating with extremely large numbers and may successfully cope with the problems of overflow associated with the calculation of large factorials involved in the analytical calculation of angular momentum group coefficients.
![symbolic calculator free download windus symbolic calculator free download windus](https://www.toddlamothe.com/wp-content/uploads/2008/11/image2.png)
In the present paper we describe the Scheme implementation of the program to calculate analytically the Clebsch–Gordan coefficients, 6 j and 9 j symbols, and general recoupling coefficients by a direct evaluation of the sum formulas. Fritzsche implemented graphical rules to generate the sum formula expressing the recoupling coefficient as a sum of products of the Wigner 6 j and/or 9 j symbols multiplied by phase and square root factors within the framework of MAPLE. Wei has developed the FORTRAN implementation of a programs' suite to calculate exactly the 3 j, 6 j and 9 j symbols. Stevenson presented the Java Applets to calculate analytically the Clebsch–Gordan coefficients and 3 j, 6 j and 9 j symbols. Recently a number of papers have been published on this topic. On the other hand, the analytical calculations (typically more slow) may produce the exact values for arbitrary large angular momenta. Since the formulas for the angular momentum group coefficients include an alternating sum, the derivation of acceptable, accurate values using floating point calculations can sometimes be challenging, especially when the angular momentum arguments are large. For such applications one is usually interested in the accurate and fast calculation routines. In general these coefficients describe an explicit transformation of the angular momenta of subsystems upon passing to different coupling schemes. When evaluating the many-particle matrix elements involving symmetric quantum operators, the general angular momentum recoupling coefficients play an important role. Among the most frequently used quantities of this theory are the Clebsch–Gordan coefficients and Wigner n – j symbols. In various branches of physics and chemistry the quantum-mechanical description of many-particle processes often relies on the quantum theory of angular momentum.
![symbolic calculator free download windus symbolic calculator free download windus](https://static.giga.de/wp-content/uploads/2017/01/Old-Calculator-for-Windows-10-Artikelbild-rcm1200x627u.jpg)
The running time for large-scale calculations depends strongly on the number and magnitude of arguments' values (i.e., of the angular momenta). Typical running time:The Clebsch–Gordan coefficients, Wigner 6 j and 9 j symbols, and general recoupling coefficients with small angular momenta are computed almost instantaneously. Restrictions on the complexity of the problem:Limited only by the DrScheme implementation used to run the program. A general angular momentum recoupling coefficient for an arbitrary number of (integer or half-integer) angular momenta is expressed as a sum over products of the Clebsch–Gordan coefficients.
![symbolic calculator free download windus symbolic calculator free download windus](https://i1.wp.com/playstoreforpcdownload.com/wp-content/uploads/2018/01/aid1882435-v4-728px-Use-Calculator-on-a-Mac-Step-18-Version-3.jpg)
Method of solution:A direct evaluation of sum formulas.
#Symbolic calculator free download windus code
The presented code provides a fast and exact calculation of the angular momentum coupling and recoupling coefficients for large values of quantum angular momenta and is based on the GNU Library General Public License PLT software. Nature of physical problem: The accurate and fast calculation of the angular momentum coupling and recoupling coefficients is required in various branches of quantum many-particle physics. of bytes in distributed program, including test data, etc.: 109 396 of lines in distributed program, including test data, etc.: 2872 Memory required to execute with typical data:50 MB (≈ size of DrScheme, version 204)
#Symbolic calculator free download windus windows
Operating systems under which the program has been tested: Windows 2000 IrelandĬomputer for which the program is designed:Any Scheme-capable platform Program obtainable from:CPC Program Library, Queen's University of Belfast, N.