Quantum Mechanics and Its Evolving Formulations.

In this paper, we discuss the time evolution of the quantum mechanics formalism. Starting from the heroic beginnings of Heisenberg and Schrödinger, we cover successively the rigorous Hilbert space formulation of von Neumann, the practical bra-ket formalism of Dirac, and the more recent rigged Hilbert space approach.

Quantification method using the Morlet wavelet for magnetic resonance spectroscopic signals with macromolecular contamination.

We study the Morlet wavelet transform on characterizing Magnetic Resonance Spectroscopic (MRS) signals acquired at short echo-time. These signals contain contributions from metabolites, water and a baseline which mainly originates from large molecules, known as macromolecules, and lipids. The baseline signal decays faster than the metabolite ones. Therefore, by making use of the time-scale representation of the wavelet, the two signals can be distinguished without any additional pre-processing. This is confirmed by the experimental results which show that the Morlet wavelet can correctly quantify the metabolite contributions even when a baseline is embedded in the MRS signals.