Exploring the Quantum Oscillator Model for Diatomic Molecules

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The discussion centers on the implications of the quantum oscillator model for diatomic molecules, particularly at absolute zero (T=0). It highlights that, according to this model, molecules possess zero point energy, indicating they retain a minimum level of vibrational energy even at 0K. This raises the question of whether molecules vibrate at T=0, despite the absence of kinetic energy. The conversation suggests that molecules are never completely at rest, challenging the concept of achieving absolute zero. The link provided seeks further clarification on these concepts.
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if the quantum oscillator was used to describe a diatomic molecule, then at T=0, the molecule shouldn't be vibrating at all. but using the quantum oscillator model, the molecule still has a minimum energy at its ground state related to its zero point energy. does this mean a molecule at T=0 DOES vibrate still?
 
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In my opinion:
This implies that molecules are not completely at rest, even at 0K. Zero point energy = minimal energy of oscillation. On the other hand 0K means no kinetic energy, so we cannot achieve 0K.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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