Effective potential and resummation procedure to multidimensional complex cubic potentials for weak and strong coupling

Abstract

The method for the recursive calculation of the effective potential is applied successfully in case of weak coupling limit (g tend to zero) to a multidimensional complex cubic potential. In strong-coupling limit (g tend to infinity), the result is resumed using the variational perturbation theory (VPT). It is found that the convergence of VPT-results approaches those expected.

Generalized Laguerre polynomials with position-dependent effective mass visualized via Wigner’s distribution functions

“…In [55] we propose a method of derivation which allow us to obtain a general integrals containing a product of two gamma functions with a monomial x m , with m ∈ N. Indeed, we show that: It is obvious that the application of (B.1) is not restricted to the present paper; many others possibilities follow in physics as well as in mathematics, see [55].…”

“…In the present appendix, we present the main result established in [55] by means of an integral, which may be useful for calculating the expectation values (4.8) and (4.10).…”

“…dx = 2dµ(x)/(α|µ(x)|) over all configuration space and ( * * ) follows after carrying out the µ 2 -integration using the relation 6.561.16 of [53]. Finally, inserting (A.6) into (A.5) and performing the s-integration using the integral established in [55] where s = p/α and ς 1,2 = l/2 + l 1,2 + 1/4. In ( * ) we have performed the µ 2 -integration using 6.561.16 of [53] and Σ…”

“…In order to carry out the sintegration in (A.8), we need once again the integral established in [55].…”

Pseudo-Hermiticity and weak pseudo-Hermiticity: Equivalence of complementarity and the coordinate transformations in position-dependent mass

“…In recent years, the concept of pseudo-Hermiticity has attracted much attention on behalf of physicists [1][2][3][4][5][6][7][8][9]. The basic mathematical structure underlying the properties of pseudo-Hermiticity is revealed [3][4][5] and it has been found to be a more general concept then those of Hermiticity and PT -symmetry [10][11][12][13][14][15]. By definition, a linear operator H (here a Hamiltonian) acting in a Hilbert space H is called η-pseudo-Hermitian if it obeys to [3][4][5] ηH = H † η,…”