الفهرس 
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Abstract
The aim of this thesis is to study the properties of
heavy and heavy-light meson in different physical systems,
by employing multi-dimensional Schrödinger equation (SE)
with the different kinds of symmetrical effective potentials.
The thesis contains four chapters and it is composed as
follows: Introduction, three chapters, and a list of the
references.
Chapter One:
In this chapter, the basic concepts and theories are
given such as the standard model, the concept of quantum
chromodynamics (QCD) theoryand its properties such as
asymptotic freedom and color-confinement. The derivation of
the N-dimensional SE and a comprehensive survey of
previous works related to the N-dimensional SE with its
applications to meson properties are introduced.
Chapter Two:
In this chapter, the effect of an extended Cornell
potential on the mass spectra of heavy and heavy-light
mesons is studied. The Cornell potential is extended to
include quadratic potential and inverse quadratic potential.
The N-radial Schrödinger equation is solved by using series
method. The results for charmonium( ̅) and bottom onium( ̅) and light-heavy meson masses such as ̅ , ̅, ̅
and ̅ are obtained. A comparison with other recent works
is discussed. The present results are improved in comparison
with other recent works and are in a good agreement with
experimental data. The results of this chapter is puplished in
Journal of Foundations and Application of Physics, vol. 6,
No. 2, (2019).
Chapter Three:
In this chapter, Generalized temperature and
anisotropy dependent Debye screening mass is introduced
into the real part of a potential in an anisotropic plasma. The
N-radial Schr ̈dinger equation (SE) is approximately solved
by using the Nikiforov-Uvarov (NU) method which based
on the expansion of power series. Binding energies and
dissociation temperatures of charmonium and bottomonium
are calculated. In addition, we have calculated the screening
mass values for different parameters. charmonium and
bottomonium binding energies within an anisotrpic meduim
are found. Also, the dissociation temperatures of both the
charmonium and the bottomonium in anisotropic medium
appear larger compoved to those found within an isotropic
medium. Finally, one observes that in any medium the
bottomonium dissociation temperature is higher than the
charmonium one. The results of this chapter is puplished in
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International Journal of modern Physics A, vol. 35, No. 21,
(2020).
Chapter Four:
In this chapter, the effects of strong magnetic field
on quark thermal medium with considering the effect of
number of flavors are studied. The N-radial Schr ̈dinger
equation (SE) is solved using Nikiforov-Uvarov’s method.
The Debye mass ( ) and the real part of heavy potential are
employed. The binding energy (BE) and the dissociation
temperatures ( ) of charmonium and bottomonium are
obtained. By increasing the magnetic field and the number of
flavors ( ), we note that the binding energy of charmonium
and bottomonium decreases, also of both ̅ and ̅
decreases. Finally, we have noted that dissociation
temperature of charmonium is higher than the bottomonium.
The effect of on the binding energy and the dissociation
temperature is noticed. The results of this chapter under
review in impact factor journal and puplished in The third
International Conference for Mathematics & Applications
(ICMA 20) 26-27 Nov. 2020, Cairo, Egypt