Studies on the perturbation problems in quantum mechanics

Download

index.pdf

Date

2004

Author

Koca, Burcu

Metadata

Show full item record

Item Usage Stats

248
views

103
downloads

In this thesis, the main perturbation problems encountered in quantum mechanics have been studied.Since the special functions and orthogonal polynomials appear very extensively in such problems, we emphasize on those topics as well. In this context, the classical quantum mechanical anharmonic oscillators described mathematically by the one-dimensional Schrodinger equation have been treated perturbatively in both finite and infinite intervals, corresponding to confined and non-confined systems, respectively.

Subject Keywords

Differential equations.

URI

http://etd.lib.metu.edu.tr/upload/12604930/index.pdf
https://hdl.handle.net/11511/14186

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Inverse problems for a semilinear heat equation with memory Kaya, Müjdat; Çelebi, Okay; Department of Mathematics (2005) In this thesis, we study the existence and uniqueness of the solutions of the inverse problems to identify the memory kernel k and the source term h, derived from First, we obtain the structural stability for k, when p=1 and the coefficient p, when g( )= . To identify the memory kernel, we find an operator equation after employing the half Fourier transformation. For the source term identification, we make use of the direct application of the final overdetermination conditions.
On the consistency of the solutions of the space fractional Schroumldinger equation (vol 53, 042105, 2012) Bayin, Selcuk S. (2012-08-01) Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.
Inverse problems for parabolic equations Baysal, Arzu; Çelebi, Okay; Department of Mathematics (2004) In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Proble...
Sturm comparison theory for impulsive differential equations Özbekler, Abdullah; Ağacık, Zafer; Department of Mathematics (2005) In this thesis, we investigate Sturmian comparison theory and oscillation for second order impulsive differential equations with fixed moments of impulse actions. It is shown that impulse actions may greatly alter the oscillation behavior of solutions. In chapter two, besides Sturmian type comparison results, we give Leightonian type comparison theorems and obtain Wirtinger type inequalities for linear, half-linear and non-selfadjoint equations. We present analogous results for forced super linear and super...
Periodic solutions and stability of differential equations with piecewise constant argument of generalized type Büyükadalı, Cemil; Akhmet, Marat; Department of Mathematics (2009) In this thesis, we study periodic solutions and stability of differential equations with piecewise constant argument of generalized type. These equations can be divided into three main classes: differential equations with retarded, alternately advanced-retarded, and state-dependent piecewise constant argument of generalized type. First, using the method of small parameter due to Poincaré, the existence and stability of periodic solutions of quasilinear differential equations with retarded piecewise constant...

Citation Formats

B. Koca, “Studies on the perturbation problems in quantum mechanics,” M.S. - Master of Science, Middle East Technical University, 2004.