Degenerate Canonical Forms of Ordinary Second-Order Linear Homogeneous Differential Equations
For each fundamental and widely used ordinary second-order linear homogeneous differential equation of mathematical physics, we derive a family of associated differential equations that share the same “degenerate” canonical form. These equations can be solved easily if the original equation is known...
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| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/2/94 |
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doaj-d28327c6baa54f88aeae4fba8c18edad2021-06-01T00:27:31ZengMDPI AGAxioms2075-16802021-05-0110949410.3390/axioms10020094Degenerate Canonical Forms of Ordinary Second-Order Linear Homogeneous Differential EquationsDimitris M. Christodoulou0Eric Kehoe1Qutaibeh D. Katatbeh2Department of Mathematical Sciences, University of Massachusetts Lowell, Lowell, MA 01854, USADepartment of Mathematics, Colorado State University, Fort Collins, CO 80523, USADepartment of Mathematics & Statistics, Jordan University of Science & Technology, Irbid 22110, JordanFor each fundamental and widely used ordinary second-order linear homogeneous differential equation of mathematical physics, we derive a family of associated differential equations that share the same “degenerate” canonical form. These equations can be solved easily if the original equation is known to possess analytic solutions, otherwise their properties and the properties of their solutions are de facto known as they are comparable to those already deduced for the fundamental equation. We analyze several particular cases of new families related to some of the famous differential equations applied to physical problems, and the degenerate eigenstates of the radial Schrödinger equation for the hydrogen atom in <i>N</i> dimensions.https://www.mdpi.com/2075-1680/10/2/94ordinary differential equationsanalytical methodsmathematical modelsRiccati equationradial Schrödinger equationtransformations |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Dimitris M. Christodoulou Eric Kehoe Qutaibeh D. Katatbeh |
| spellingShingle |
Dimitris M. Christodoulou Eric Kehoe Qutaibeh D. Katatbeh Degenerate Canonical Forms of Ordinary Second-Order Linear Homogeneous Differential Equations Axioms ordinary differential equations analytical methods mathematical models Riccati equation radial Schrödinger equation transformations |
| author_facet |
Dimitris M. Christodoulou Eric Kehoe Qutaibeh D. Katatbeh |
| author_sort |
Dimitris M. Christodoulou |
| title |
Degenerate Canonical Forms of Ordinary Second-Order Linear Homogeneous Differential Equations |
| title_short |
Degenerate Canonical Forms of Ordinary Second-Order Linear Homogeneous Differential Equations |
| title_full |
Degenerate Canonical Forms of Ordinary Second-Order Linear Homogeneous Differential Equations |
| title_fullStr |
Degenerate Canonical Forms of Ordinary Second-Order Linear Homogeneous Differential Equations |
| title_full_unstemmed |
Degenerate Canonical Forms of Ordinary Second-Order Linear Homogeneous Differential Equations |
| title_sort |
degenerate canonical forms of ordinary second-order linear homogeneous differential equations |
| publisher |
MDPI AG |
| series |
Axioms |
| issn |
2075-1680 |
| publishDate |
2021-05-01 |
| description |
For each fundamental and widely used ordinary second-order linear homogeneous differential equation of mathematical physics, we derive a family of associated differential equations that share the same “degenerate” canonical form. These equations can be solved easily if the original equation is known to possess analytic solutions, otherwise their properties and the properties of their solutions are de facto known as they are comparable to those already deduced for the fundamental equation. We analyze several particular cases of new families related to some of the famous differential equations applied to physical problems, and the degenerate eigenstates of the radial Schrödinger equation for the hydrogen atom in <i>N</i> dimensions. |
| topic |
ordinary differential equations analytical methods mathematical models Riccati equation radial Schrödinger equation transformations |
| url |
https://www.mdpi.com/2075-1680/10/2/94 |
| work_keys_str_mv |
AT dimitrismchristodoulou degeneratecanonicalformsofordinarysecondorderlinearhomogeneousdifferentialequations AT erickehoe degeneratecanonicalformsofordinarysecondorderlinearhomogeneousdifferentialequations AT qutaibehdkatatbeh degeneratecanonicalformsofordinarysecondorderlinearhomogeneousdifferentialequations |
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1721414913043202048 |