Clasical and quantum harmonic oscillator - correspondence principle

In summary, the classical and quantum harmonic oscillators are two important models used to understand the behavior of systems that exhibit oscillatory motion. The correspondence principle states that the predictions made by the classical model should match those of the quantum model in the limit of large values for certain variables. This principle serves as a bridge between the classical and quantum worlds and helps us understand the connections between the two theories.
  • #1
exponent137
561
33
At classical harmonic oscillator, total energy is proportional to square of frequency, but at quantum harmonic oscillator, total energy is proportional to frequency.
Are those two frequencies the same?
How it is with transition from quantum harmonic oscillator to classical harmonic oscillator? How omega^1 and omega^2 agree?

One example of this is http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc6.html
but where is the frequency?

Maybe I found answer:
http://en.wikipedia.org/wiki/Correspondence_principle
Is this enough?
 
Last edited:
Physics news on Phys.org
  • #2
The next question is:
How more simply to imagine formula W = (n+1/2)ω ?
W is energy ω is frequency and n is integer quantum number.
The common calculation for quantum oscillator is too long for such short result.
 
  • #3
Does relativistic generalization of quantum harmonic oscillator exist?
Maybe:
http://www.quantumsciencephilippines.com/1811/lowest-order-relativistic-energy-correction-of-1-d-harmonic-oscillator/
 
Last edited:

What is the correspondence principle in classical and quantum harmonic oscillators?

The correspondence principle states that in the classical limit, the behavior of a quantum system should approach and agree with the classical behavior. In the case of harmonic oscillators, this means that as the quantum number increases, the energy levels of the quantum system should approach and match the energy levels of the classical system.

How do classical and quantum harmonic oscillators differ?

Classical harmonic oscillators follow the laws of classical mechanics, while quantum harmonic oscillators follow the laws of quantum mechanics. This leads to differences in their behavior, such as discrete energy levels in quantum systems versus continuous energy levels in classical systems.

What is the relationship between the frequency of a classical oscillator and the energy of a quantum oscillator?

The frequency of a classical oscillator is directly proportional to the energy of a quantum oscillator. This relationship is known as the energy-frequency correspondence and is a key aspect of the correspondence principle.

How does the correspondence principle apply to other systems besides harmonic oscillators?

The correspondence principle is a fundamental concept in quantum mechanics and applies to all systems. It states that the behavior of a quantum system should approach and agree with the behavior of a classical system in the classical limit, regardless of the specific system being studied.

Why is the correspondence principle important in understanding the relationship between classical and quantum mechanics?

The correspondence principle helps bridge the gap between classical and quantum mechanics by showing that in the classical limit, the two approaches agree and can be used interchangeably. It also highlights the limitations of classical mechanics and the need for a quantum description of the microscopic world.

Similar threads

I Doubt on Morse potential and harmonic oscillator
    • Quantum Physics
Replies
2
Views
994
B Frequency of an EM wave in Classical and Quantum Physics
    • Quantum Physics
Replies
6
Views
820
I Frequency of EM waves in classical and quantum physics
    • Quantum Physics
Replies
26
Views
2K
A Cause of spontaneous emission?
    • Quantum Physics
Replies
15
Views
2K
I Understanding No Energy Degeneracy in Sakurai's Quantum Mechanics
    • Quantum Physics
Replies
2
Views
1K
I Classical vs. Quantum Defintion of Energy in Field Theory
    • Quantum Physics
Replies
3
Views
2K
I Question about the quantum harmonic oscillator
    • Quantum Physics
Replies
7
Views
2K
I Classical field in quantum field theory?
    • Quantum Physics
Replies
4
Views
1K
A Feynman propagator for a simple harmonic oscillator
    • Quantum Physics
Replies
9
Views
3K
I Is the ground state energy of a quantum field actually zero?
    • Quantum Physics
4
Replies
113
Views
10K

Hot Threads

Recent Insights

Back
Top