as the energy of the quantum harmonic oscillator increases fluctuations in probability density become more dense and hence no matter how short the interval over which they are averaged there will be some energy level at which the average is equal to the classical time-spent probability density function.

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As the energy of the quantum harmonic oscillator increases fluctuations in probability density become more dense and hence no matter how short the interval over which they are averaged there will be some energy level at which the average is equal to the classical time-spent probability density function.