Range of validity of the Schrodinger equation

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Discussion Overview

The discussion revolves around the range of validity of the Schrödinger equation, particularly in relation to various types of waves, including sound waves, water waves, and waves on springs. Participants explore the applicability of the equation in both microscopic and macroscopic contexts, as well as the limitations encountered in practical scenarios.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants assert that the Schrödinger equation is applicable to the behavior of matter and electromagnetic waves at the microscopic scale, but question its relevance to everyday wave phenomena like sound and water waves.
  • One participant provides links suggesting that the Schrödinger equation fails in certain everyday situations, indicating a limitation in its applicability.
  • Another participant proposes that familiar types of waves, such as sound waves and elastic waves, can be quantized and are described by the concept of phonons, while specific studies on surface capillary waves have introduced the term "ripplons."
  • It is suggested that the Schrödinger equation remains valid as long as relativistic effects are negligible, particularly in scenarios without spin-orbit interactions or high-speed particles, although practical solutions for large systems like water molecules are challenging.
  • One participant emphasizes that while the Schrödinger equation theoretically governs the behavior of water waves, solving it accurately for large systems often requires additional empirical parameters.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the Schrödinger equation to various wave phenomena, with some asserting its limitations in everyday contexts while others argue for its broader relevance. The discussion remains unresolved regarding the extent of its validity in these scenarios.

Contextual Notes

Limitations include the complexity of solving the Schrödinger equation for large systems and the dependence on specific conditions such as the absence of relativistic effects. The discussion highlights the challenges in applying quantum mechanics to macroscopic phenomena.

spaghetti3451
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I understand that the Schrödinger equation describes the behaviour of matter and the electromagnetic wave down to the microscopic scale. But I'm not sure about the everyday sound waves, water waves, wave on a spring, etc. What do you think?
 
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failexam, I think what you're asking is, "Are these other, more familiar, types of waves quantized also?" And the answer is yes, although the description is usually more complicated, since a large number of particles is involved.

Quanta of sound waves (pressure waves in a gas) and all kinds of elastic waves such as waves on a spring are lumped together under the term phonons. Surface capillary waves on liquid He4 have been studied, and given the name "ripplons".
 
failexam said:
I understand that the Schrödinger equation describes the behaviour of matter and the electromagnetic wave down to the microscopic scale. But I'm not sure about the everyday sound waves, water waves, wave on a spring, etc. What do you think?

It is valid as long as there is no significant relativistic effect. That is to say, anything that does not involve spin-orbit interaction, heavy atoms, or near light speed particles, Schrödinger equation is accurate as long as the correct hamiltonian operator is supplied.

The equation it self describes perfectly behavior of matter to macroscopic scale and yes the property of water waves is ultimately governed by Schrödinger equation. However, it is simply not possible to solve this equation to satisfactory accuracy for such large systems (it is already not quite solvable for 500 water molecules). For these model theories with additional empirical parameters have to be used.
 

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