Bound state solutions of the Schrödinger equation for potentials with dirac delta functions
| dc.contributor | Ph.D. Program in Physics. | |
| dc.contributor.advisor | Demiralp, Ersan. | |
| dc.contributor.author | Uncu, Haydar. | |
| dc.date.accessioned | 2023-03-16T10:46:01Z | |
| dc.date.available | 2023-03-16T10:46:01Z | |
| dc.date.issued | 2007. | |
| dc.description.abstract | A general method for the bound state solutions of the SchrÄodinger equation for analytically solvable potentials with any ¯nite number of Dirac delta functions is intro- duced for n-dimensional systems. Then, the potentials with Dirac delta functions are used to model some physical systems. The eigenvalue equations for harmonic and linear potentials with a ¯nite number of Dirac delta functions located randomly are derived for one dimensional systems. For the latter potential, the behavior of the eigenvalues of the ground and the ¯rst excited states for various strengths and locations of Dirac delta functions is investigated. The eigenvalues and the number of bound states for a PT -symmetric system with two Dirac delta functions are studied. In case of a contact interaction, to get the changes from a liner potential, the changes in the masses of s states for charmonium is presented. It is also shown that the Fermi energy of a trian- gular well changes if there is an impurity in the well. By describing a dimple potential with a Dirac delta function, it is shown that tight and deep dimple potentials can in- crease the condensate fraction and critical temperature of a Bose-Einstein condensate. We conclude that addition of the point interactions which can be modelled by Dirac delta functions changes the properties of the physical systems considerably. | |
| dc.format.extent | 30cm. | |
| dc.format.pages | xii, 99 leaves; | |
| dc.identifier.other | PHYS 2007 U63 PhD | |
| dc.identifier.uri | https://digitalarchive.library.bogazici.edu.tr/handle/123456789/13753 | |
| dc.publisher | Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2007. | |
| dc.relation | Includes appendices. | |
| dc.relation | Includes appendices. | |
| dc.subject.lcsh | Schrödinger equation. | |
| dc.subject.lcsh | Dirac equation. | |
| dc.title | Bound state solutions of the Schrödinger equation for potentials with dirac delta functions |
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