Probability density doesn't oscillate with time

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Discussion Overview

The discussion revolves around the behavior of probability density in quantum mechanics, specifically addressing why it does or does not oscillate with time. The scope includes theoretical explanations and clarifications regarding stationary states and general states.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions why the probability density does not oscillate with time.
  • Another participant asserts that probability density can oscillate, particularly in stationary states, and seeks clarification on the situation.
  • A participant explains that in a stationary state, the probability density remains constant over time due to the nature of the wavefunction, which evolves but results in a time-independent probability density.
  • It is noted that the probability density of a general state does evolve over time because it is a superposition of multiple eigenfunctions.
  • A later reply acknowledges the clarification about stationary states and expresses a need for more information to fully address the original question.
  • Another participant provides links to animations demonstrating time-varying probability densities.

Areas of Agreement / Disagreement

Participants generally agree that the probability density of a stationary state does not oscillate with time, but there is a lack of consensus on the broader implications for general states and the original question posed by the OP.

Contextual Notes

The discussion includes assumptions about the definitions of stationary and general states, as well as the mathematical treatment of wavefunctions and probability densities, which may not be fully resolved.

solas99
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why the probability density doesn't oscillate with time?
 
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It can do - and usually does, for instance, in a stationary state.
What is the situation.
 
For a stationary state the probability density does not oscillate in time.

The wavefunction of a stationary state does evolve in time according to ψ(x,t)=f(x)e-iEt, where f(x) is an eigenfunction of the Hamiltonian, and E is the corresponding eigenvalue. However, the probability density is the "square" of the wavefunction, ψψ*, where the multiplication of e-iEt with the complex conjugatate of eiEt gives e0=1, which doesn't change with time.

The probability density of a general state does evolve in time, because it is the superposition of several eigenfunctions.
 
Last edited:
Oh I get you - I misread.
Yeah - the probability density of a stationary state does not vary with time, which is sort-of why it is a stationary state.
Still need more info to answer OPs question properly.
 
Last edited by a moderator:

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