Topics re harmonic oscillators

[radiogaga35]

Hi there

I've heard from various applied mathematicians that the D.E. that models harmonic motion is one of the most important in physics...apparently it appears in nearly every conceivable field, from quantum mechanics to cosmology (something to do with modelling the cosmic microwave background)?

Accordingly I've decided that it might be beneficial if I tried to read widely on harmonic oscillators.

I'm a first-year physics/appl. maths major. I've covered Feynman's treatment of the topic (Lectures Vol. I chapters 21-24 I think) and other than that I've encountered it, though on a basic level, in my introductory mechanics and statistical mechanics courses.

Is the harmonic oscillator really as important as I've heard? And if so, could you recommend with which topics I might start and how I could proceed? Also, if I could use this as a platform to get to grips with some new math (or at least, math I would encounter only later in my studies) then that would be a bonus...

Thanks in advance!

 

[fikus]

Yes harmonic oscillator is indeed a very imoprtant topic in physics.
First of all because all potentials near equilibrium are in first order approximate quadratic (what is exactly potential of harmonic oscillator). As we know all thing in nature are usually in equilibrium and any displacements from that state can be treated as harmonic motions.
Second of all harmonic oscillator is one of the few examples that can be solved in analytic way.

It can be found in all books of mathemathical physics and of course in books of classical mechanics (Goldstein...). Quantum harmonic oscollator can be found in all introductionary books of quantum mechanics.

Hope that helps.

 

[radiogaga35]

Ok, thanks for the suggestions...sounds like I'm spoilt for choice!