Approximate Analytical Solutions of the Klein-Gordon Equation for Hulthen Potential with Position-Dependent Mass

The Klein-Gordon equation is solved approximately for the Hulth\'{e}n potential for any angular momentum quantum number $\ell$ with the position-dependent mass. Solutions are obtained reducing the Klein-Gordon equation into a Schr\"{o}dinger-like differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get an energy eigenvalue and and the wave functions. It is found that the results in the case of constant mass are in good agreement with the ones obtained in the literature.Comment: 15 pages, two table

Approximate Analytical Solutions of the Effective Mass Dirac Equation for the generalized Hulthen Potential with any kappa-Value

The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulth\'{e}n potential with any spin-orbit quantum number $\kappa$. Solutions are obtained by using an appropriate coordinate transformation, reducing the effective mass Dirac equation to a Schr\"{o}dinger-like differential equation. The Nikiforov-Uvarov method is used in the calculations to obtain energy eigenvalues and the corresponding wave functions. Numerical results are compared with those given in the literature. Analytical results are also obtained for the case of constant mass and the results are in good agreement with the literature.Comment: 13 page

Bound state solution of the Schrodinger equation for Mie potential

Exact solution of Schrodinger equation for the Mie potential is obtained for an arbitrary angular momentum. The energy eigenvalues and the corresponding wavefunctions are calculated by the use of the Nikiforov-Uvarov method. Wavefunctions are expressed in terms of Jacobi polynomials. The bound states are calculated numerically for some values of l and $n$ with n<5. They are applied to several diatomic molecules.Comment: 10 page

Non-extensive study of Rigid and Non-rigid Rotators

The isotropic rigid and non-rigid rotators in the framework of Tsallis statistics are studied in the high and low temperature limits. The generalized partition functions, internal energies and heat capacities are calculated. It has been found that results are in well agreement with the classical Boltzmann-Gibbs statistics in the limiting Tsallis index. It has also been observed that nonextensivity parameter q behaves like a scale parameter in the low temperature regime.Comment: 11 Pages, 3 Figures, Late

Approximate Pseudospin and Spin Solutions of the Dirac Equation for a Class of Exponential Potentials

Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $\kappa$ in the case of spin and pseudospin symmetry, respectively. We have approximated for non s-waves the centrifugal term by an exponential form. The energy eigenvalue equations, and the corresponding wave functions are obtained by using the generalization of the Nikiforov-Uvarov method.Comment: 14 page

Prunella vulgaris l. ve prunella grandiflora l.’den saflaştırılan rosmarinik asitin farklı tümör hücreleri üzerindeki sitotoksik aktivitesi

Rosmarinic acid was isolated from ethanol extractions obtained from Prunella grandiflora L. and P. vulgaris L. The total phenolic content of ethanol fractions during isolation was determined by the Folin-Ciocateu method. The cytotoxic doses of the isolated rosmarinic acid were determined by WST-1 (Roche Applied Sciences, Mannheim, Germany) cell proliferation assay. A 10-60ng cytotoxic dose was determined for pancreas (PANC-1), prostate (PC-3), colon (HT-29) and breast (MDAMB 436) cancers and GBM (T98G) cell lines and lymphatic tissues. 24 and 48h incubation periods were applied during dose determinations. An antiproliferative effect was observed at the end of 48h incubation period with 50ng rosmaniric acid treatment in PC3 cell line and with 60ng treatment in PANC-1, HT-29, MDA-MB 436 and T98G cell lines. No cytotoxic activity of rosmarinic acid was observed in non-tumor cells.Bu çalışmada rosmarinik asit bileşiği, Prunella grandiflora L. ve P. vulgaris L. türlerinden elde edilen etanol ekstraktlarından saflaştırılmıştır. Saflaştırma işlemi sırasında elde edilen metanol fraksiyonlarının toplam fenol içeriği FolinCiocalteu yöntemi ile belirlenmiştir. Prunella L. türlerinden saflaştırılan rosmarinik asitin farklı kanser hücreleri üzerinde WST-1 (Roche Applied Sciences, Mannheim, Almanya) yöntemiyle sitotoksik doz çalışmaları yapılmıştır. Buna göre pankreas (PANC-1), prostat (PC-3), kolon (HT-29) ve meme (MDA-MB 436) kanserleri ile GBM (T98G) hücre hatları ve lenf dokularında 10-60ng arasında sitotoksik doz belirlenmiştir. Sitotoksik doz belirleme çalışmaları için 24 ve 48 saat inkübasyon süreleri çalışılmıştır. 48 saat inkübasyon süresi sonunda PC3 hücre hattı için 50ng ve PANC-1, HT-29, MDA-MB 436 ve T98G hücre hatları için 60ng rosmarinik asit uygulamasında antiproliferatif etki gözlenmiştir. Sağlıklı hücrelerde rosmarinik asitin sitotoksik etkisi gözlenmemiştir

Exact solution of Schrodinger equation for modified Kratzer's molecular potential with the position-dependent mass

Exact solutions of Schrodinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the corresponding eigenfunctions are calculated for any angular momentum for target potentials. Various forms of point canonical transformations are applied. PACS numbers: 03.65.-w; 03.65.Ge; 12.39.Fd Keywords: Morse potential, Kratzer potential, Position-dependent mass, Point canonical transformation, Effective mass Schr\"{o}dinger equation.Comment: 9 page

Effective Mass Dirac-Morse Problem with any kappa-value

The Dirac-Morse problem are investigated within the framework of an approximation to the term proportional to $1/r^2$ in the view of the position-dependent mass formalism. The energy eigenvalues and corresponding wave functions are obtained by using the parametric generalization of the Nikiforov-Uvarov method for any $\kappa$-value. It is also studied the approximate energy eigenvalues, and corresponding wave functions in the case of the constant-mass for pseudospin, and spin cases, respectively.Comment: 12 page

Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential

The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations by choosing a mass distribution.Comment: 10 page

Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics

Using the NU method [A.F.Nikiforov, V.B.Uvarov, Special Functions of Mathematical Physics, Birkhauser,Basel,1988], we investigated the real eigenvalues of the complex and/or $PT$- symmetric, non-Hermitian and the exponential type systems, such as Poschl-Teller and Morse potentials.Comment: 14 pages, Late