A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension

Please use this identifier to cite or link to this item: https://hdl.handle.net/10646/3456

Title:	A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension
Authors:	Muchatibaya, Gift Fassari, S. Rinaldi, F. Mushanyu, Josiah giftmuchatibaya@gmail.com
Keywords:	Hamiltonian Gaussian attractive potential artificial atoms harmonic oscillator
Issue Date:	7-Feb-2016
Publisher:	Hindawi Publishing Corporation
Citation:	Muchatibaya, G., Fassari, S., Rinaldi, F., & Mushanyu, J. (2016). A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension. Advances in Mathematical Physics, 2016. DOI: http://dx.doi.org/10.1155/2016/2125769
Abstract:	The ground state energy 𝐸 0(𝜆) of 𝐻 𝜆 = − 𝑑 2 /𝑑𝑥 2 − 𝜆 𝑒 −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 𝜖 0 ( 𝜆 ) = \| 𝐸 0 (𝜆)\| 1/2 is the root
URI:	http://hdl.handle.net/10646/3456
ISSN:	1687-9139
Appears in Collections:	Department of Mathematics Staff Publications

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