Eigenvalues of Particle Bound in Single and Double Delta Function Potentials through Numerical Analysis
This study employs the use of the fourth order
Numerov scheme to determine the eigenstates and eigenvalues of
particles, electrons in particular, in single and double delta function
potentials. For the single delta potential, it is found that the
eigenstates could only be attained by using specific potential depths.
The depth of the delta potential well has a value that varies depending
on the delta strength. These depths are used for each well on the
double delta function potential and the eigenvalues are determined.
There are two bound states found in the computation, one with a
symmetric eigenstate and another one which is antisymmetric.
[1] C. Kittel, "Introduction to Solid State Physics 8th Edition," USA: John
Wiley & Sons Inc., 2005, pp. 169-176
[2] D. Griffiths, "Introduction to Quantum Mechanics," New Jersey:
Prentice Hall, Inc., 1995, pp. 50-59
[3] A. Blom, "Computer Algorithms for Solving the Schrödinger and
Poisson equations," Division of Solid State Theory, Department of
Physics, Lund University. Sölvegatan 14 A, S-223 62 Lund, Sweden.
December 2, 2002
[4] P. Harrison, "QUANTUM WELLS, WIRES AND DOTS. Theoretical
and Computational Physics of Semiconductor Nanostructures, 2nd ed,"
England: John Wiley & Sons, LTD. 2005, pp. 73-79
[5] The Root Team, "Root An Object-Oriented Data Analysis Framework
Users Guide 5.26." December 2009
[6] S. Gasiorowicz, "Quantum Physics, 3rd ed." USA: John Wiley & Sons,
Inc. 2003, pp. 81-84
[7] S. Cahn, G. Mahan, and B. Nadgorny, "A GUIDE TO PHYSICS
PROBLEMS part 2 Thermodynamics, Statistical Physics, and Quantum
Mechanics," New York: Kluwer Academic/Plenum Publishers. 1997,
pp. 248-249
[1] C. Kittel, "Introduction to Solid State Physics 8th Edition," USA: John
Wiley & Sons Inc., 2005, pp. 169-176
[2] D. Griffiths, "Introduction to Quantum Mechanics," New Jersey:
Prentice Hall, Inc., 1995, pp. 50-59
[3] A. Blom, "Computer Algorithms for Solving the Schrödinger and
Poisson equations," Division of Solid State Theory, Department of
Physics, Lund University. Sölvegatan 14 A, S-223 62 Lund, Sweden.
December 2, 2002
[4] P. Harrison, "QUANTUM WELLS, WIRES AND DOTS. Theoretical
and Computational Physics of Semiconductor Nanostructures, 2nd ed,"
England: John Wiley & Sons, LTD. 2005, pp. 73-79
[5] The Root Team, "Root An Object-Oriented Data Analysis Framework
Users Guide 5.26." December 2009
[6] S. Gasiorowicz, "Quantum Physics, 3rd ed." USA: John Wiley & Sons,
Inc. 2003, pp. 81-84
[7] S. Cahn, G. Mahan, and B. Nadgorny, "A GUIDE TO PHYSICS
PROBLEMS part 2 Thermodynamics, Statistical Physics, and Quantum
Mechanics," New York: Kluwer Academic/Plenum Publishers. 1997,
pp. 248-249
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63797", author = "Edward Aris D. Fajardo and Hamdi Muhyuddin D. Barra", title = "Eigenvalues of Particle Bound in Single and Double Delta Function Potentials through Numerical Analysis", abstract = "This study employs the use of the fourth order
Numerov scheme to determine the eigenstates and eigenvalues of
particles, electrons in particular, in single and double delta function
potentials. For the single delta potential, it is found that the
eigenstates could only be attained by using specific potential depths.
The depth of the delta potential well has a value that varies depending
on the delta strength. These depths are used for each well on the
double delta function potential and the eigenvalues are determined.
There are two bound states found in the computation, one with a
symmetric eigenstate and another one which is antisymmetric.", keywords = "Double Delta Potential, Eigenstates, Eigenvalue,
Numerov Method, Single Delta Potential", volume = "5", number = "12", pages = "2129-3", }