A note on the discrete spectrum of Gaussian wells. I: The ground state energy in one dimension (Q1796534)

Summary: The ground state energy \(E_0(\lambda)\) of \(H_\lambda = - d^2 / d x^2 - \lambda e^{- x^2}\) is computed for small values of \(\lambda\) by means of an approximation of an integral operator in momentum space. Such an approximation leads to a transcendental equation for which \(\epsilon_0(\lambda) = | E_0(\lambda) |^{1 / 2}\) is the root.