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Approximate
Energy Spectra
of the Quantum
Gaussian Well: A
Four-parameter
Potential
Fitting
Mahmoud Farouta, Ayham
Shaera
and
Sameer
M. Ikhdaira,b
a
Physics
Department,
Faculty of
Science, An-
Najah National
University,
Nablus, West
Bank, Palestine.
b
Department
of Electrical
Engineering,
Near East
University,
Nicosia,
Northern Cyprus,
Mersin 10,
Turkey.
Corresponding
Author: Mahmoud
Farout
Email:
m.qaroot@najah.edu
Doi: https://doi.org/10.47011/15.5.6
Cited by :
Jordan J. Phys.,
15 (5) (2022)
487-494
PDF
Received
on:
11/03/2021;
Accepted
on:
13/06/2021
Abstract:
In this
work, we
present
a
detailed
study of
a
one-dimensional
Schrödinger
equation
in the
presence
of
quantum
Gaussian
well
interaction.
Further,
we
investigate
the
approximate
solutions
by using
the
harmonic
oscillator
approximation,
variational
principle,
four-parameter
potential
fitting
and
numerical
solution
using
the
finite-difference
method.
The
parabolic
approximation
yields
an
excellent
energy
value
compared
with the
numerical
solution
of the
Gaussian
system
only for
the
ground
state,
while
for the
excited
states,
it
provides
a higher
approximation.
Also,
the
analytical
bound-state
energies
of the
four-parameter
potential
under
the
framework
of the
Nikiforov-Uvarov
(NU)
method
have
been
used
after
getting
the
suitable
values
of the
potential
parameters
using
numerical
fitting.
The
present
results
of the
system
states
are
found to
be in
high
agreement
with the
well-known
numerical
results
of the
Gaussian
potential.
Keywords:
Gaussian
potential,
One-dimensional
Schrödinger
equation,
Nikiforov-
Uvarov
(NU)
method,
Four-parameter
potential.
PACS:
03.65.−w;
02.90.+p;
12.39.Pn.
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