Revision as of 18:59, 6 February 2016 (view source) Apm (Talk | contribs) (symbolic math roughly finished) ← Older edit		Revision as of 19:00, 6 February 2016 (view source) Apm (Talk | contribs) m (→‎Math: -n) Newer edit →
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−	Let us define "quantumness" as the ration of the energy quantisation (the minimum allowed energy steps) to the average thermal energy in a single degree of freedom: <br>	+	Let us define "quantumness" as the ratio of the energy quantisation (the minimum allowed energy steps) to the average thermal energy in a single degree of freedom: <br>
	Quantumness: <math> Q = \frac{\Delta E}{E_T} </math> <br>		Quantumness: <math> Q = \frac{\Delta E}{E_T} </math> <br>
	First we'll need the thermal energy: <br>		First we'll need the thermal energy: <br>

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Revision as of 19:00, 6 February 2016

Math

Let us define "quantumness" as the ratio of the energy quantisation (the minimum allowed energy steps) to the average thermal energy in a single degree of freedom:
Quantumness:

$$Q = \frac{\Delta E}{E_T}$$
First we'll need the thermal energy:
Equipartitioning: $$E_T = \frac{1}{2}k_BT \quad$$
The size of the energy quanta depends on the system under consideration.

Reciprocative linear motion

The uncertainty relation:

$$\Delta x \Delta p \geq h \quad$$ Newton: $$\Delta E = \frac{\Delta p^2}{2m} \quad$$
Quantumness: $$Q = \frac{h^2}{k_B} \frac{1}{m \Delta x^2 T}$$

Reciprocative circular motion

The uncertainty relation:

$$\alpha \Delta L \geq h \quad$$ Newton: $$\Delta E = \frac{\Delta L^2}{2I} \quad$$
Quantumness: $$Q = \frac{h^2}{k_B} \frac{1}{I \alpha^2 T}$$

Values

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Discussion

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