I Understanding the Irreducible Solution in Classical Harmonic Oscillators

George444fg
Messages
25
Reaction score
4
TL;DR Summary
Harmonic Oscillator
Hellow. I am doing an introductory to Quantum Mechanics course, and the irreducible solution appeared in the harmonic oscillator. When we talk about the irreducible solution, this is the solution as a linear combination of the eigenbasis of the system. This is understandable, however, if I have a simple case of a harmonic oscillator, with solution sin(wt) then the irreducible solution would be ie^(-iwt)? Thank you in advance
 
Physics news on Phys.org
I'm a little confused by the terminology you use, particularly irreducible solution. But I read your post as defining the irreducible solution as the solution written as the sum of eigenvectors. Also, are you referring to the quantum harmonic oscillator or the classical harmonic oscillator in the last half of your post?
 
Haborix said:
I'm a little confused by the terminology you use, particularly irreducible solution. But I read your post as defining the irreducible solution as the solution written as the sum of eigenvectors. Also, are you referring to the quantum harmonic oscillator or the classical harmonic oscillator in the last half of your post?
It is the classic oscillator. But nonetheless, it can be derived from the quantum oscillator.
 
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
Back
Top