A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension
The ground state energy E0(λ) of Hλ=-d2/dx2-λe-x2 is computed for small values of λ by means of an approximation of an integral operator in momentum space. Such an approximation leads to a transcendental equation for which ϵ0(λ)=|E0(λ)|1/2 is the root.
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/2125769 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832554963675381760 |
|---|---|
| author | G. Muchatibaya S. Fassari F. Rinaldi J. Mushanyu |
| author_facet | G. Muchatibaya S. Fassari F. Rinaldi J. Mushanyu |
| author_sort | G. Muchatibaya |
| collection | DOAJ |
| description | The ground state energy E0(λ) of Hλ=-d2/dx2-λe-x2 is computed for small values of λ by means of an approximation of an integral operator in momentum space. Such an approximation leads to a transcendental equation for which ϵ0(λ)=|E0(λ)|1/2 is the root. |
| format | Article |
| id | doaj-art-7241f15953a84dbe8b7e19438f4d3aa9 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-7241f15953a84dbe8b7e19438f4d3aa92025-02-03T05:49:56ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/21257692125769A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One DimensionG. Muchatibaya0S. Fassari1F. Rinaldi2J. Mushanyu3Department of Mathematics, University of Zimbabwe, P.O. Box MP167, Mount Pleasant, Harare, ZimbabweUniversitá Degli Studi Guglielmo Marconi, Via Plinio 44, 00193 Rome, ItalyUniversitá Degli Studi Guglielmo Marconi, Via Plinio 44, 00193 Rome, ItalyDepartment of Mathematics, University of Zimbabwe, P.O. Box MP167, Mount Pleasant, Harare, ZimbabweThe ground state energy E0(λ) of Hλ=-d2/dx2-λe-x2 is computed for small values of λ by means of an approximation of an integral operator in momentum space. Such an approximation leads to a transcendental equation for which ϵ0(λ)=|E0(λ)|1/2 is the root.http://dx.doi.org/10.1155/2016/2125769 |
| spellingShingle | G. Muchatibaya S. Fassari F. Rinaldi J. Mushanyu A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension Advances in Mathematical Physics |
| title | A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension |
| title_full | A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension |
| title_fullStr | A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension |
| title_full_unstemmed | A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension |
| title_short | A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension |
| title_sort | note on the discrete spectrum of gaussian wells i the ground state energy in one dimension |
| url | http://dx.doi.org/10.1155/2016/2125769 |
| work_keys_str_mv | AT gmuchatibaya anoteonthediscretespectrumofgaussianwellsithegroundstateenergyinonedimension AT sfassari anoteonthediscretespectrumofgaussianwellsithegroundstateenergyinonedimension AT frinaldi anoteonthediscretespectrumofgaussianwellsithegroundstateenergyinonedimension AT jmushanyu anoteonthediscretespectrumofgaussianwellsithegroundstateenergyinonedimension AT gmuchatibaya noteonthediscretespectrumofgaussianwellsithegroundstateenergyinonedimension AT sfassari noteonthediscretespectrumofgaussianwellsithegroundstateenergyinonedimension AT frinaldi noteonthediscretespectrumofgaussianwellsithegroundstateenergyinonedimension AT jmushanyu noteonthediscretespectrumofgaussianwellsithegroundstateenergyinonedimension |