Lecture in Quantum Mechanics -- Ehrenfest theorem (part2) and evolution operator
Lecture in Quantum Mechanics -- Ehrenfest theorem (part2) and evo…
Nov 7, 2020
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Ehrenfest's theorem states that for a particle for which the un... | Filo
Ehrenfest's theorem states that for a particle for which the un... | Filo
8 months ago
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The Ehrenfest theorem and the classical limit d(p)/dt = 0 (1) T... | Filo
The Ehrenfest theorem and the classical limit d(p)/dt = 0 (1) T... | Filo
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3K views · 180 reactions | Classical and Quantum Physics describe reality in completely different ways. Yet, in 1927, Paul Ehrenfest showed how Newton's equation could be derived from Schrödinger's, establishing a deep continuity in our understanding of the physical universe. Join Brian Greene for a brief explanation of Ehrenfest's essential idea as well as the mathematical manipulations he required to realize it. | World Science Festival | Facebook
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SOLVED:(a) Using Equation 4.190 and the generalized Ehrenfest theorem (3.73), show that (d⟨𝐫⟩)/(d t)=(1)/(m)⟨(𝐩-q 𝐀)⟩. Hint: This stands for three equations-one for each component. Work it out for, say, the x component, and then generalize your result. (b) As always (see Equation 1.32 ) we identify d⟨𝐫⟩/ d t with ⟨𝐯⟩. Show that^59 m (d⟨𝐯⟩)/(d t)=q⟨𝐄⟩ (q)/(2 m)⟨(𝐩 ×𝐁-𝐁 ×𝐩)⟩-(q^2)/(m)⟨(𝐀 ×𝐁)⟩. (c) In particular, if the fields E and B are uniform over the volume of the wave packet, sho
SOLVED:(a) Using Equation 4.190 and the generalized Ehrenfest the…
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