https://doi.org/10.1140/epjp/i2016-16308-y
Regular Article
Position-dependent mass approach and quantization for a torus Lagrangian
Department of Physics, Faculty of Science, Gazi University, 06500, Ankara, Turkey
* e-mail: yesiltas@gazi.edu.tr
Received:
30
June
2016
Revised:
21
July
2016
Accepted:
10
August
2016
Published online:
9
September
2016
We have shown that a Lagrangian for a torus surface can yield second-order nonlinear differential equations using the Euler-Lagrange formulation. It is seen that these second-order nonlinear differential equations can be transformed into the nonlinear quadratic and Mathews-Lakshmanan equations using the position-dependent mass approach developed by Mustafa (J. Phys. A: Math. Theor. 48, 225206 (2015)) for the classical systems. Then, we have applied the quantization procedure to the nonlinear quadratic and Mathews-Lakshmanan equations and found their exact solutions.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016
