Range of validity of the Schrodinger equation

In summary, the Schrodinger equation describes the behavior of matter and electromagnetic waves on a microscopic scale. However, it is also applicable to everyday sound waves, water waves, and waves on a spring, although the description may be more complicated due to a larger number of particles being involved. This equation is accurate as long as there are no significant relativistic effects, such as spin-orbit interaction or near light speed particles. For larger systems, model theories with empirical parameters are often used.
  • #1
spaghetti3451
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I understand that the Schrodinger 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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  • #3
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".
 
  • #4
failexam said:
I understand that the Schrodinger 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, schrodinger 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 schrodinger 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.
 

1. What is the range of validity of the Schrodinger equation?

The Schrodinger equation is a fundamental equation in quantum mechanics that describes the behavior of particles at the atomic and subatomic level. Its range of validity extends to all physical systems, from individual particles to complex molecules.

2. Does the Schrodinger equation apply to all particles?

Yes, the Schrodinger equation is applicable to all particles, including electrons, protons, and neutrons. It also applies to particles with mass and those without, such as photons.

3. What factors affect the range of validity of the Schrodinger equation?

The Schrodinger equation is based on several assumptions, such as the non-relativistic nature of particles and the absence of external forces. These factors can limit its range of validity in certain situations.

4. Can the Schrodinger equation accurately predict the behavior of particles at all timescales?

No, the Schrodinger equation is limited in its ability to accurately predict the behavior of particles at very small or very large timescales. At these extremes, other equations, such as the Dirac equation or quantum field theory, may be more appropriate.

5. How does the Schrodinger equation relate to the uncertainty principle?

The Schrodinger equation is a key component of the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle simultaneously. The equation describes the probability distribution of a particle's position and momentum, and this inherent uncertainty is a fundamental aspect of quantum mechanics.

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