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7 months ago in Quantum Mechanics By Rani
How does schrödinger’s equation become f = ma?
We're told quantum mechanics reduces to classical physics at large scales. But can you actually show Schrödinger's equation turning into Newton's laws, or is it just a philosophical hand-wave?
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By Payal G Answered 1 month ago
You can show it—Ehrenfest's Theorem is the bridge. It proves that the expectation values of position and momentum follow equations that look exactly like Newton's laws: d⟨p⟩/dt = ⟨−∇V⟩, and ⟨v⟩ = d⟨x⟩/dt = ⟨p⟩/m. If the wave packet stays narrow and the potential doesn't vary wildly over its width, these expectation values follow classical trajectories. The math is clean. Quantum becomes classical when you stop looking at the spread and start tracking the average.
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