Range of validity of the Schrodinger equation

[spaghetti3451]

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?

 

[atyy]

The Schroedinger equation fails in these everyday situations:
http://www.fourmilab.ch/documents/golden_glow/
http://www.desy.de/user/projects/Physics/Relativity/SR/gold_color.html
http://focus.aps.org/story/v27/st2

 

[Bill_K]

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".

 

[virtualzx]

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.