The classical behaviour of a quantum ensemble is expected to be achievable only by a limiting procedure. In this communication we discuss two remarkable examples in which position and momentum probability density functions using an arbitrary Gaussian ensemble (described by a non-coherent Gaussian wave packet) develop identically both in classical and quantum mechanics. The first case is propagation in free space and the second in a harmonic oscillator potential. In both cases quantum potential and quantum force (defined in Bohm's theory) are non-zero. This may be stated to be the outcome of the present investigation.
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