According to Rayleigh, if one sets a linear oscillator in motion in a viscous fluid, the fluid not only opposes the motion with a velocity‐dependent dissipative force, but the fluid accretes to the oscillator changing its effective mass. A perturbation linking a mass accretion operator with the usual complex spontaneous decay operator is applied to a nonrelativistic quantum undamped oscillator. It results in a quantum model of Rayleigh’s oscillator for which the equation of motion for the expectation value of position and the Heisenberg uncertainty relation between the position and linear momentum are the anticipated ones for a quantum mechanical underdamped oscillator. Another model based on a variation of these ideas which allows for all possibilities, no change or diminution or accretion, for the perturbed mass is presented for the critically damped oscillator. In both models, the situation is fixed by the experimental dissipative ‘‘forces.’’

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