کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1856168 | 1529878 | 2013 | 17 صفحه PDF | دانلود رایگان |
• We apply supersymmetric quantum mechanics to the inverted oscillator potential.
• The complex second-order transformations allow us to build new non-singular potentials.
• The algebraic structure of the initial and final potentials is analyzed.
• The initial potential is described by a complex-deformed Heisenberg–Weyl algebra.
• The final potentials are described by polynomial Heisenberg algebras.
In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in particular, only very specific second-order transformations produce non-singular real potentials. It will be shown that these transformations turn out to be the so-called complex ones. Moreover, we will study the factorization method applied to the inverted oscillator and the algebraic structure of the new Hamiltonians.
Journal: Annals of Physics - Volume 333, June 2013, Pages 290–306