The ground state energy 𝐸_0(𝜆) of 𝐻_𝜆= −𝑑^2/𝑑𝑥^2 − 𝜆𝑒^−𝑥^2 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.
A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension
Rinaldi F;
2016-01-01
Abstract
The ground state energy 𝐸_0(𝜆) of 𝐻_𝜆= −𝑑^2/𝑑𝑥^2 − 𝜆𝑒^−𝑥^2 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.File in questo prodotto:
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