Quantum mechanics on curved hypersurfaces

Olpak, Mehmet Ali
In this work, Schrödinger and Dirac equations will be examined in geometries that confine the particles to hypersurfaces. For this purpose, two methods will be considered. The first method is the thin layer method which relies on explicit use of geometrical relations and the squeezing of a certain coordinate of space (or spacetime). The second is Dirac’s quantization procedure involving the modification of canonical quantization making use of the geometrical constraints. For the Dirac equation, only the first method will be considered. Lastly, the results of the two methods will be compared and some notes on the differences between the results will be included.


Hamilton-Jacobi theory of continuous systems
Güler, Y. (Springer Science and Business Media LLC, 1987-8)
The Hamilton-Jacobi partial differnetial equation for classical field systems is obtained in a 5n-dimensional phase space and it is integrated by the method of characteristics. Space-time partial derivatives of Hamilton’s principal functionsS μ (Φ i ,x ν ) (μ,ν=1,2,3,4) are identified as the energy-momentum tensor of the system.
Pseudospin symmetry solution of the Dirac equation with an angle-dependent potential
Berkdemir, Cueneyt; Sever, Ramazan (IOP Publishing, 2008-02-01)
The pseudospin symmetry solution of the Dirac equation for spin 1/2 particles moving within the Kratzer potential connected with an angle-dependent potential is investigated systematically. The Nikiforov-Uvarov method is used to solve the Dirac equation. All of the studies are performed for the exact pseudospin symmetry (SU2) case and also the exact spin symmetry case is given briefly in the appendix. Bound-state solutions are presented to discuss the contribution of the angle-dependent potential to the rel...
Numerical studies of the electronic properties of low dimensional semiconductor heterostructures
Dikmen, Bora; Tomak, Mehmet; Department of Physics (2004)
An efficient numerical method for solving Schrödinger's and Poisson's equations using a basis set of cubic B-splines is investigated. The method is applied to find both the wave functions and the corresponding eigenenergies of low-dimensional semiconductor structures. The computational efficiency of the method is explicitly shown by the multiresolution analysis, non-uniform grid construction and imposed boundary conditions by applying it to well-known single electron potentials. The method compares well wit...
Dual Killing-Yano symmetry and multipole moments in electromagnetism and mechanics of continua
Baleanu, D; Dubovik, VM; Misicu, S (1999-10-01)
In this work we introduce the Killing-Yano symmetry on the phase space and we investigate the symplectic structure on the space of Killing-Yano tensors. We perform the detailed analyze of the n-dimensional flat space and the Riemaniann manifolds with constant scalar curvature. We investigate the form of some multipole tensors, which. arise in the expansion of a system of charges and currents, in terms of second-order Killing-Yano tensors in the phase space of classical mechanics. We find some relations betw...
Exact supersymmetric solution of Schrödinger equation for some potentials
Aktaş, Metin; Sever, Ramazan; Department of Physics (2005)
Exact solution of the Schrödinger equation with some potentials is obtained. The normal and supersymmetric cases are considered. Deformed ring-shaped potential is solved in the parabolic and spherical coordinates. By taking appropriate values for the parameter q, similar results are obtained for Hulthén and exponential type screened potentials. Similarly, Morse, Pöschl-Teller and Hulthén potentials are solved for the supersymmetric case. Supersymmetric solution of PT-/non-PT-symmetric and non-Hermitian Mors...
Citation Formats
M. A. Olpak, “Quantum mechanics on curved hypersurfaces,” M.S. - Master of Science, Middle East Technical University, 2010.