General formula for finding Mexican hat wavelets by virtue of Dirac's representation theory and coherent state

Mexican hat 型势的 Raleigh-Ritz 方法的严格检验

Rigorous test of the Raleigh-Ritz method for Mexican hat type potentials

本文严格检验 Raleigh-Ritz 方法在 Mexican hat 型非简谐势中的适用性，表明此类模型具有闭式精确基态，可作为 Higgs 场的量子力学玩具模型。

Lamb's reconstruction of potentials and spatially localized scattering in nonrelativistic quantum mechanics

We formulate a simple condition for reconstructibility of a certain class of Hamiltonians with real potentials from the knowledge of their complex-valued eigenfunctions. This may be relevant to the question of preparability of quantum states raised by W. Lamb in his 1969 paper on operational interpretation of quantum mechanics. Of particular interest to engineering applications are: (a) an exotic case of an upside-down harmonic-oscillator-type potential (a variation of the inverted "Mexican hat" potential) whose square-integrable complex eigenfunction describes a localized scattering state sim…