It is the classic oscillator. But nonetheless, it can be derived from the quantum oscillator.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?
An irreducible state solution is a concept in physics that refers to a state in which a system cannot be broken down into smaller, more fundamental parts. This means that the system is in a stable and unchanging state, and cannot be further simplified or reduced.
The concept of irreducible state solution is important because it helps us understand the behavior of complex systems. By identifying and studying these states, we can gain insights into the underlying principles and laws that govern the behavior of the system as a whole.
Scientists use various methods and techniques, such as mathematical modeling and experimental observations, to identify irreducible state solutions. These methods involve analyzing the behavior and interactions of the system's components to determine if they can be further reduced or simplified.
Examples of systems that exhibit irreducible state solutions include simple physical systems like a pendulum or a simple harmonic oscillator, as well as complex systems like weather patterns, ecosystems, and the human brain.
In most cases, an irreducible state solution is considered to be stable and unchanging. However, in some cases, external factors or disturbances can cause a system to shift to a new irreducible state solution. This is known as a phase transition and is an area of active research in physics.