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One of the results arising from quantum mechanics is that energy is quantized for a particle. In particular, the translational energy levels are quantized.

  • Is it fair to say that the translational energy levels of a macroscopic object are also quantized, but in such a way that the degree of separation between the energy levels is negligible ?

Additional Information:

My understanding of the translational energy of a particle is that, it can only occupy a discrete set of energy levels.

For example if we were to model the particle moving along the positive part of $x$ axis, its translational energy levels would be more akin to

$$f(x)=\lfloor{x} \rfloor$$ rather than $$f(x)=x$$.

Is this interpretation correct?

Iamat8
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J.Gudal
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    The energy of a free particle is not discrete, the spectrum of $H = \frac{p^2}{2m}$ is completely continuous. You'll have to give more context for what you're talking about. – ACuriousMind Dec 28 '15 at 18:50
  • OK I shall clarify. – J.Gudal Dec 28 '15 at 18:51
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    Your understanding is incorrect; in general, energy is discrete for a bound particle, but continuous for a free one. – Javier Dec 28 '15 at 19:03
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    @Javier Thanks. This is probably a stupid question but what is the distinction between a bound particle and free one? – J.Gudal Dec 28 '15 at 19:05
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    @J.Gudal: e.g. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/pbox.html#c3. Particles with energy $E>U_0$ are free particles, particles with $E<U_0$ are bound particles. For bound particles there has to be a potential energy well. – Gert Dec 28 '15 at 19:17

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