Linked Questions

67
votes
5answers
16k views

Why is the harmonic oscillator so important?

I've been wondering what makes the harmonic oscillator such an important model. What I came up with: It is a (relatively) simple system, making it a perfect example for physics students to learn ...
19
votes
2answers
2k views

“QFT is simple harmonic motion taken to increasing levels of abstraction”

"QFT is simple harmonic motion taken to increasing levels of abstraction." This is my memory of a quote from Sidney Coleman, which is probably in many textbooks. What does it refer to, if he meant ...
14
votes
2answers
3k views

How to derive the theory of quantum mechanics from quantum field theory?

I have read the book on quantum field theory for some time, but I still do not get the physics underline those tedious calculations. The thing confused me most is how quantum mechanics relates to ...
6
votes
1answer
670 views

Making precise the statement “particles are excitations in a quantum field”

I've been trying to self teach QFT lately. I find that the basic physical idea makes sense, and I can keep up with the mathematical formalism without too much trouble, but I'm having trouble ...
2
votes
0answers
2k views

Fourier mode expansion of quantum fields

My question pertains to understanding the notion of Fourier modes in the context of quantum fields. For simplicity I have stuck to free scalar fields. As I understand it, to solve the (homogeneous) ...
4
votes
3answers
442 views

What is the relationship between vibration of the field and quantum fluctuation?

Consider a free field like the KG equation. I see that why $$\tilde \phi(\mathbf{p},t)$$ a momentum-dependent quantity, is an oscillator, vibrating at a frequency because when we apply the Fourier ...
1
vote
2answers
206 views

What is the precise formal correspondance between an oscillator and a quantum field?

A common route of introduction to quantum field theory is to note a similarity between the mathematical structure of a quantum harmonic oscillator and of a quantum field "at a point". The quantised ...
2
votes
0answers
412 views

Why is the quantum harmonic oscillator model used when an electromagnetic field is quantised?

I'm reading textbooks for quantum optics, and then see that every textbook introduces the quantisation of light, for which each book employs the quantum harmonic oscillator model. Why is this ...
0
votes
2answers
239 views

The “harmonic paradigm” in physics

Disclaimer: I know this is a vague question, so if this is not the appropriate thread, please direct me to the correct one. On page 5 of Anthony Zee's Quantum Field Theory in a Nutshell he speaks of ...
1
vote
0answers
77 views

Why does light come as quanta of the harmonic oscillator?

I've recently been learning the basics of Quantum optics and it seems to be a fundamental concept that light is best described in the framework of the Quantum Harmonic Oscillator. This lead to a ...