Probability of zero in stationary wave state

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Discussion Overview

The discussion revolves around the concept of stationary waves in quantum mechanics, specifically addressing the phenomenon of zero probability at certain points in stationary wave states. Participants explore the implications of probability density and the conditions that lead to these zero probability locations.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the reason behind zero probability at specific points in stationary wave states, seeking a deeper understanding of the underlying principles.
  • Another participant suggests that there may be confusion between probability density and probability, proposing that the term "stationary waves" might refer to "plane waves" which describe particles with definite energy and momentum.
  • A different participant clarifies that "stationary wave" likely refers to a stationary state or energy eigenstate, which is independent of time under a time-independent Hamiltonian.
  • A participant reiterates the initial question about the cause of zero probability at certain points, providing an analogy with a vibrating string in its second harmonic, noting that the center does not move.
  • One participant asserts that the cause of zero probability is related to boundary and continuity/smoothness conditions.

Areas of Agreement / Disagreement

Participants express differing interpretations of the terminology used, particularly regarding the distinction between probability and probability density. There is no consensus on the explanation for zero probability locations, as various factors are proposed without resolution.

Contextual Notes

Participants have not fully clarified the definitions of terms such as "stationary waves" and "probability density," which may affect the understanding of the discussion. The relationship between boundary conditions and probability outcomes remains an area of exploration.

knightpraetor
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What is it that causes the probability of stationary waves ( or waves in general) to be zero at a particular point? I mean, when i look at a stationary wave state there are places that there are zero probability of the particle being at with a particular energy, but i don't understand why there is zero probability there
 
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I'm sure you're confusing the probability density with the probability itself. By "stationary waves" (in QM perhaps) do you mean "plane waves" ? They describe particles with definite energy & momentum.

Daniel.
 
By stationary wave, I think he/she means stationary state: i.e. an energy eigenstate (which is, therefore, independent of time, assuming a time-independent Hamiltonian).
 
knightpraetor said:
What is it that causes the probability of stationary waves ( or waves in general) to be zero at a particular point? I mean, when i look at a stationary wave state there are places that there are zero probability of the particle being at with a particular energy, but i don't understand why there is zero probability there
Take a high speed photo of a vibrating string in its second harmonic.
The center will never move.
 
And as for the "what causes it..." part of the question, the answer is simple: boundary & continuity/smoothness conditions.
 

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