State space of a standing wave?

Click For Summary

Discussion Overview

The discussion revolves around the concept of defining a 'state-space' for the frequencies of a standing wave, particularly in the context of wave mechanics and harmonic oscillators. Participants explore the relationship between state-space concepts and the behavior of standing waves in strings.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests that a state is defined by the minimal amount of independent variables needed to describe a system, referencing (q,p)-phase-space for point masses and Hilbert-space for quantum states.
  • Another participant questions whether the original concept of "phase space" is derived from wave or harmonic oscillator motions.
  • A subsequent reply seeks clarification on whether the previous response implies agreement with the idea of defining a state-space for frequencies.
  • Another participant proposes considering the governing equation for the motion of a standing wave as a way to further explore the concept of state-space.

Areas of Agreement / Disagreement

Participants express varying interpretations of the relationship between phase space and standing waves, indicating that multiple competing views remain without a clear consensus.

Contextual Notes

The discussion does not resolve the assumptions regarding the definitions of state-space or the governing equations for standing waves, leaving these aspects open for further exploration.

pliep2000
Messages
5
Reaction score
1
Lets say a state is defined by the minimal amount of independent variables to completely describe a system.
One would come up with the (q,p)-phase-space for a point mass and as another example the Hilbert-space for quantum-states.

Consider the very simple case of a standing wave in string where f1, f2 etc are the fundamental and the harmonics.

Question: Could one define a 'state-space' of the frequencies f1, f2 etc.?
 
Physics news on Phys.org
Doesn't the original concept behind "phase space" pretty much come from wave/harmonic oscillator motions?
 
Do i interpret your answer correctly as: yes probably?
 
Well, maybe you can think of it this way:
Suppose you were to write down a governing equation for the motion of the standing wave in a string. What would such an equation look like?
 

Similar threads

Undergrad Representation of Spin 1/2 quantum state
  • · Replies 61 ·
3
Replies
61
Views
6K
Undergrad Qubit two-state quantum system
  • · Replies 29 ·
Replies
29
Views
2K
Undergrad Postulate of only time dependence on |ψ⟩
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Does the quantum space of states have countable or uncountable basis?
  • · Replies 67 ·
3
Replies
67
Views
7K
Undergrad Quantum particle's state in momentum eigenfunctions basis
  • · Replies 16 ·
Replies
16
Views
2K
Graduate Wave-packet in configuration space
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Understanding Spin States in 2D Vector Spaces
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Operators in finite dimension Hilbert space
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Can a wave-function be a combination of states with different energies?
  • · Replies 18 ·
Replies
18
Views
2K
Undergrad Mean values of observables
  • · Replies 2 ·
Replies
2
Views
1K