On the other hand, the analytical calculations (typically more slow) may produce the exact values for arbitrary large angular momenta. Recently a number of papers have been published on this topic. Stevenson presented the Java Applets to calculate analytically the Clebsch–Gordan coefficients and 3 j, 6 j and 9 j symbols. Wei has developed the FORTRAN implementation of a programs' suite to calculate exactly the 3 j, 6 j and 9 j symbols. 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. 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. 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. The program offers a platform-independent graphical user front end which allows a user-friendly calculation of the coefficients under consideration. In Section 2 we present the expressions employed in calculating the coefficients. Section 3 describes the structure of the program. The use of the program itself is described in Section 4. 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 program Scheme2Clebsch is written up in the language Scheme according to the formulas described above. #Symbolic calculator free download windus windows.#Symbolic calculator free download windus code.
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