A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension
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
Additional Citation Information
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/10.1155/2016/2125769Publisher
Hindawi Publishing Corporation