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 ...
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 ...
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 ...
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 ...
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) ...
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 ...
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 ...
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 ...