Particles in an energy eigenstate not moving?

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A particle in an energy eigenstate is described by a wavefunction that does not change its probability distribution over time, indicating it is in a stationary state. This means that while the particle has a defined energy, it does not exhibit classical motion, as its position is not changing in a probabilistic sense. The wavefunction's time evolution can be expressed as a multiplication by a phase factor, which does not affect the overall probability density. Consequently, expectation values for position and momentum remain constant in stationary states. Therefore, a particle in an energy eigenstate cannot be considered to be moving in the classical sense.
sheelbe999
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I'm really struggling with this one guys, the question is:

Explain why a particle which is in an energy eigenstate cannot be moving in the
classical sense.
 
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What you need to know to answer this is a) the interpretation of a wavefunction, and b) how a wavefunction changes with time. (If you know that the state at t=0 is f, then what is it at arbitrary t? f(t)=(something)f, right?).

(This should probably be in the homework forum).
 
thanks and will move it

henry
 
Hints: This has to do with "stationary states".

What is a prerequisite for a stationary state? What do stationary states imply for expectation values?
 
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
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