Can the 1D Wave Equation Accurately Describe dΨ(x)/dt?

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Discussion Overview

The discussion centers around the question of whether the 1D wave equation can be used to describe the time derivative of a wave function, denoted as dΨ(x)/dt. The scope includes theoretical considerations related to wave functions and their mathematical representation in quantum mechanics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about the applicability of the 1D wave equation for describing dΨ(x)/dt.
  • Another participant seeks clarification on the definition of ##\psi(x)##, suggesting it refers to a wave function.
  • A third participant asserts that the Schrödinger equation is more appropriate for describing wave functions rather than an arbitrary wave equation, noting that the suitability of a 1D description depends on the symmetry of the system.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate mathematical framework for describing dΨ(x)/dt, with some favoring the 1D wave equation and others advocating for the Schrödinger equation. The discussion remains unresolved regarding the best approach.

AleksanderPhy
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Hello!
So if I want to describe dΨ(x)/dt can I use 1D wave equation?
 
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What is ##\psi(x)##?
 
blue_leaf77 said:
What is ##\psi(x)##?
1D wave function
 
Then you will describe it using Schroedinger equation, not an arbitrary wave equation. Whether it can be described using 1D space, it depends on the symmetry of the system at hand.
 

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