phy(ac circuit)

The mean value in Quantum Mechanics is the average result obtained when a large number of measurements are made on identical systems, i.e. systems in the same state |y(t)>.

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The mean value of X and P in an eigenstate of H is always zero.
The classical mean value can be defined as the average result obtained when a large number of measurements are made on the same system at different times, or when a large number of measurements are made at the same time on different systems, whose phases are randomly chosen.

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Consider a harmonic oscillator of well-defined energy.
For a harmonic oscillator of well-defined energy
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But we have to remember that the classical and quantum mechanical mean value are interpreted differently.
In a similar way the quantum mechanical and the classical root-mean-square deviation are interpreted differently.
In Quantum Mechanics we define

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for n=0, i.e. for the ground state.
For a classical harmonic oscillator with energy
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we have

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The quantum mechanical root mean square deviations
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are proportional to the classical maximum amplitude and maximum momentum.
The classical root-mean-square deviation is given by

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For a harmonic oscillator of well defined energy we obtain the same root-mean-square deviations. But again we have to remember that the classical and quantum mechanical root-mean-square deviation are interpreted differently

駛唔駛咁深奧阿, 多餘

So Professional For Mr.Ho Fook Leong.

2009-08-13 17:49:46 補充：
So Bad For 冷風's Comment.Its Bad.