Continuous wavelet transform analysis of one-dimensional quantum ground states (Q2715893)

The authors show that `moment quantization methods', when combined with a moment equation reformulation of the one-dimensional Schrödinger equation, can be used to generate the wavelet transform, and to reconstruct a solution. Two approaches are proposed for the reconstruction of the wave function. The first uses the wavelet transform combined with available wavelet-signal reconstruction formulas. The second reconstruction procedure is manifestly wavelet independent and makes use of certain asymptotic relations.NEWLINENEWLINENEWLINEThe principal objective is to show how the `eigenvalue moment method' can be used to generate the coefficients for the recovery of the wave functions. The formalism is applied to two problems, the quartic anharmonic oscillator and the rational fraction potential, \(V(x) = gx^6(1+\lambda x^2)\). The analysis is limited to ground state.NEWLINENEWLINEFor the entire collection see [Zbl 0911.00013].