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Micellar aqueous solutions of ionic surfactants have been observed to exhibitproton delocalization (the nuclear quantum effect) and to oscillate between alow density (LDL) and a high density (HDL) state of water state at a fixedtemperature. It is shown in this paper that such phenomena can be explainedwith the help of the interpolating Schr\"odinger equation proposed by Ghose(Ghose, 2002). The nuclear quantum effect can be described by the tunneling ofa harmonic oscillator in a symmetric double-well potential, and an ensemble ofharmonic oscillators can model the LDL-HDL oscillations. The thermodynamics ofsuch harmonic oscillators has been worked out showing continuous transitionsbetween the quantum and classical limits.

Relationship between classical and quantum mechanics in micellar aqueous solutions of surfactants