Quantum Mechanics & Superposition State Dynamics

einstein1921
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Structure and dynamics in the microcosm are inherently connected by the laws of quantum mechanics.
Take, for example, a particle put in a superposition of its
ground state
0
x of energy W 0
and the first excited
state
1
x of energy W 1
. Such a superposition state is
referred to as a wave packet. Change in the position of
its center of mass is the closest quantum mechanical ana-log of classical motion. Solution of the Schrödinger
equation for the particle’s wave function x yields an
oscillatory motion with the oscillation period T
osc
=2 / W , where W = W 1
− W 0
. The larger the energy
separation W between the two eigenstates, the faster is
the particle’s motion in the superposition state.
would you please explain why?
 

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The larger the energy
separation W between the two eigenstates, the faster is
the particle’s motion in the superposition state.
The oscillation of the wave function is faster, but whether the individual particle moves faster is not so clear. Why do you think so?
 
If you want to google "quantum beats" you'll find all sorts of careful examples with useful pictures to help understand it. To understand what's going on with "speed" or the particle, use the Fourier transform to look at the momentum-space wave function rather than the position space one.
 
Einstein Mcfly said:
If you want to google "quantum beats" you'll find all sorts of careful examples with useful pictures to help understand it. To understand what's going on with "speed" or the particle, use the Fourier transform to look at the momentum-space wave function rather than the position space one.
thank you for your answer!

if wavefunctionψ=Ʃcψ(r)exp(-i/hEt)
h should be h bar,but I cant't enter it!
what the form of momentum-space wave function?
best wishes!
 
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
Is it possible, and fruitful, to use certain conceptual and technical tools from effective field theory (coarse-graining/integrating-out, power-counting, matching, RG) to think about the relationship between the fundamental (quantum) and the emergent (classical), both to account for the quasi-autonomy of the classical level and to quantify residual quantum corrections? By “emergent,” I mean the following: after integrating out fast/irrelevant quantum degrees of freedom (high-energy modes...

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