# Java^{TM}Clebsch-Gordan Coefficient Calculator

`[*]`The calculator evaluates Clebsch-Gordan coefficients which arise in the theory of angular momentum in quantum mechanics. The arguments should be given as half-integers, in decimal form, or as integers.

`[*]`The Clebsch-Gordan coefficient calculated is, in a frequently used notation, <j_{1}m_{1}j_{2}m_{2}|jm>, which denotes that j_{1} couples with j_{2} to j, and the magnetic quantum numbers (projections along the *z*-axis) of these 3 vectors are m_{1}, m_{2} and m, respectively. The phase is that of Condon and Shortley.

`[*]`As a reminder, the following conditions apply:

- All the
*m* quantum numbers must be projections of their respective *j* values (that is, if a *j* is integral, then so must its *m* be, likewise for odd-integral *j* and *m*, and each *m* satisfies |*m*|<=*j*).
- The angular momentum vectors must satisfy the triangle relation: |
*j*_{1}-*j*_{2}|<*j* and |*j*_{1}+*j*_{2}|>*j*
*m*_{1}+*m*_{2}=*m*

`[*]`The calculator uses java classes and methods which appear only in Java 1.1 and higher, therefore your JVM will need to support this. Recent versions of Netscape and Internet Explorer both support Java 1.1 so if you are using one of these products, and the applet doesn't appear properly, you may need to upgrade.

`[*]`The answer is given as an analytic expression in the first text box, and as a decimal expansion in the second in case exactness is not requisite. If the arguments are large, the analytic expression will be long and you will need to scroll the text box to see the full expression. To save time, it is not fully simplified except for small(ish) cases.

`[*]`If you find any problems, please email me at the address below.

paul stevenson <p.stevenson@surrey.ac.uk>
Last modified: Mon Apr 30 14:36:04 BST 2001