Foundations | An-Najah Staff

Topological Considerations in Quantum Theory

Mon, 2014-02-17 13:40 — Sami Mohammad AL-Jaber

Journal Title, Volume, Page:

II Nuovo Cimento B Series 11, Volume 107, Issue 1, pp 23-37

Year of Publication:

1992

Link:

http://link.springer.com/article/10.1007%2FBF02726880

Authors:

S. M. Al-Jaber

Department of Physics and Molecular Science Program, Southern Illinois University at Carbondale, 62901, Carbondale, IL, USA

Current Affiliation:

Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine

[email protected]

W. C. Henneberger

Department of Physics and Molecular Science Program, Southern Illinois University at Carbondale, 62901, Carbondale, IL, USA

Preferred Abstract (Original):

We consider the most general case of the restricted rigid rotor, controlled by passive mechanical devices located at θ=0 and θ=π. The purpose of these devices is to restrict the particle motion to a domain of a covering space (0,Mπ), whereM is an odd integer. This system, which is not a Hamiltonian one on the physical space (0, 2π), is compared with a Hamiltonian system having delta function barriers at θ=0 and θ=π. The case ofM an even integer is also discussed by using only one mechanical device at θ=0. This non-Hamiltonian system is compared with a Hamiltonian system having a delta function barrier at θ=0. It is shown that many of the wave functions of the non-Hamiltonian systems are the same as those of the Hamiltonian ones, with an average reflection coefficient of 1/(M+1) for oddM and 2/M for evenM, which are the classical values. We show how, in the case of very largeM, the superposition principle leads to de Broglie resonances.

Some Remarks On Approximation Methods For Quantum Systems In Higher Space Dimensions

Wed, 2011-02-09 17:04 — Sami Mohammad AL-Jaber

Journal Title, Volume, Page:

Journal of the Association of Arab Universities for Basic and Applied Sciences Volume 9, Issue 1, October 2010, Pages 18-22

Year of Publication:

2010

Link:

http://www.sciencedirect.com/science/article/pii/S1815385210000064

Authors:

Sami M. Al-Jaber

Palestine Technical University, Kadoorie, Tulkarm, Palestine

Current Affiliation:

Department of Physics, Faculty of Sciences, An-Najah National University, Palestine

[email protected]

Preferred Abstract (Original):

We consider the effect of space dimension N, on the results predicted by two approximation techniques applied on physical quantum systems. In the first, we apply degenerate perturbation theory to perturbed N-dimensional infinite cubical well. It is found that the energy difference for splitting decreases as N increases and it vanishes in the infinite dimensional space. In the second, we apply the sudden approximation to the electronic structure change implied by beta-decay of the tritium nucleus. It is found that as N increases the ionization probability increases.

On The Radial Part Equation of The Wave Function In N Dimensions

Fri, 2010-04-16 23:56 — Sami Mohammad AL-Jaber

Journal Title, Volume, Page:

IL. Nuovo Cimento, 112B, No. 5, 761

Year of Publication:

1997

Authors:

Sami M. Al-Jaber

Department of Physics, Faculty of Sciences, An-Najah National University, Palestine

Current Affiliation:

Department of Physics, Faculty of Sciences, An-Najah National University, Palestine

[email protected]

Preferred Abstract (Original):

We consider the equation for the radial part of the wave function of the Schrodinger equation in the N-dimensional space. A new effective potential is derived when the equation for the radial part of the wave function is written in the form of a one-dimensional Schrodinger equation. As a constructive example, we find and discuss the solution, the orthonormality, and the energy eigenvalues of the radial part of the wave function for an infinite spherical potential well in N dimensions.

The fine structure of the N-dimensional hydrogen atom

Fri, 2010-04-16 23:46 — Sami Mohammad AL-Jaber

Journal Title, Volume, Page:

Il Nuovo Cimento B, Volume 113, Issue 05, p.651

Year of Publication:

1998

Link:

http://adsabs.harvard.edu/abs/1998NCimB.113..651A

Authors:

Sami M. Al-Jaber

Department of Physics, Faculty of Sciences, An-Najah National University, Palestine

Current Affiliation:

Department of Physics, Faculty of Sciences, An-Najah National University, Palestine

[email protected]

Preferred Abstract (Original):

The fine structure of energy levels of a hydrogen atom in N dimensions is given. This is done by calculating the first-order energy corrections due to the relativistic correction to kinetic energy, spin-orbit coupling, and Darwin term. Thus we emphasize the role of the topological structure of the configuration space of a physical system on the quantum nature of an observable of the system.

A Confined N-Dimensional Harmonic Oscillator

Tue, 2010-04-13 00:50 — Sami Mohammad AL-Jaber

Journal Title, Volume, Page:

Int. J. Theor. Phys., Vol. 47, no.7, 1853-1864.

Year of Publication:

2008

Link:

http://link.springer.com/article/10.1007%2Fs10773-007-9630-9

Authors:

Sami M. Al-Jaber

Department of Physics, An-Najah National University, Nablus, Palestine

Current Affiliation:

Department of Physics, An-Najah National University, Nablus, Palestine

[email protected]

Preferred Abstract (Original):

We compute the energy eigenvalues for the N-dimensional harmonic oscillator confined in an impenetrable spherical cavity. The results show their dependence on the size of the cavity and the space dimension N. The obtained results are compared with those for the free N-dimensional harmonic oscillator, and as a result, the notion of fractional dimensions is pointed out. Finally, we examine the correlation between eigenenergies for confined oscillators in different dimensions

Harmonic Oscillator In An Impenetrable, N-Dimensional Spherical Well

Tue, 2010-04-13 00:47 — Sami Mohammad AL-Jaber

Journal Title, Volume, Page:

Union Arab Journal., Vol.6, p.1-13

Year of Publication:

2008

Authors:

Sami M. Al-Jaber

Department of Physics, Faculty of Science, An- Najah National University, Nablus, Palestine

Current Affiliation:

Department of Physics, Faculty of Sciences, An-Najah National University, Palestine

[email protected]

Preferred Abstract (Original):

Sami M. Al-Jaber