Z. Naturforsch. **68a,** 646 – 650
(2013)

doi:10.5560/ZNA.2013-0044

An Application of Gröbner Basis in Differential Equations of Physics

Mohammad
Saleh Chaharbashloo^{1},
Abdolali
Basiri^{1},
Sajjad
Rahmany^{1}, and
Saber
Zarrinkamar^{2}

^{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.