Z. Naturforsch. 68a, 646 – 650
An Application of Gröbner Basis in Differential Equations of Physics
1 School of Mathematics and Computer Science, Damghan University, Damghan, Iran
2 Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar,Iran
Received April 9, 2013 / revised May 31, 2013 / published online August 21, 2013
We apply the Gröbner basis to the ansatz method in quantum mechanics to obtain the energy eigenvalues and the wave functions in a very simple manner. There are important physical potentials such as the Cornell interaction which play significant roles in particle physics and can be treated via this technique. As a typical example, the algorithm is applied to the semi-relativistic spinless Salpeter equation under the Cornell interaction. Many other applications of the idea in a wide range of physical fields are listed as well.
Key words: Gröbner Basis; Quantum Mechanics; Ansatz Method.