Linked Questions

5
votes
2answers
124 views

Why are sinusoids so common in nature? [duplicate]

When we are introduced to waves in school, we are often presented with a picture of a sinusoid (or a cosinusoid). Sinusoids can represent the way many physics phenomena behave, still.... Why are ...
2
votes
0answers
107 views

Why is the potential always quadratic in nature? [duplicate]

Quadratic potential is a good approximation for the minima of smooth functions. This is I think is the reason that simple harmonic motion is so common. What is the reason behind this?
1
vote
1answer
93 views

Why are oscillations so ubiquitous in nature? [duplicate]

I'm aware that you can always approximate a potential by a quadratic term. But is this the most 'fundamental' reason for the pervasiveness for oscillations?
18
votes
3answers
4k views

In what sense is a quantum field an infinite set of harmonic oscillators?

In what sense is a quantum field an infinite set of harmonic oscillators, one at each space-time point? When is it useful to think of a quantum field this way? The book I'm reading now, QFT by ...
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
3answers
273 views

Why are so many energies represented by $\frac{1}{2} ab^2$? [duplicate]

Why are so many energies in our universe mathematically represented by the equation $\frac{1}{2}ab^2$. For example: Kinetic energy $$\frac{1}{2}mv^2$$ Energy stored in a capacitor $$\frac{1}{2}CV^2$...
12
votes
1answer
2k views

Can Hooke's law be derived?

Can we derive Hooke's law from the theory of elasticity? I know it is not a fundamental law and therefore can be derived from more basic considerations.
1
vote
5answers
2k views

Fermionic quantum harmonic oscillator

Maybe stupid questions! But: Why do we need fermionic HOs? And what do they describe? And how do we come up with the Hamiltonian $$ H=\frac{1}{2} [c^\dagger,c]~? $$
13
votes
1answer
472 views

Why is the wave equation so pervasive?

The homogenous wave equation can be expressed in covariant form as $$ \Box^2 \varphi = 0 $$ where $\Box^2$ is the D'Alembert operator and $\varphi$ is some physical field. The acoustic wave ...
4
votes
4answers
792 views

What does Hooke's law have to do with molecular forces?

In The Feynman Lectures, in the chapter Characteristics of Force, In the section entitled Molecular forces, Feynman talks about the molecular forces, and then he states afterwards: If the molecules ...
12
votes
1answer
856 views

Why does a damped quantum harmonic oscillator have the same decay rate as the equivalent classical system?

$\newcommand{ket}[1]{|#1\rangle} \newcommand{bbraket}[3]{\langle #1 | #2 | #3 \rangle}$ Why does the decay rate for a damped quantum harmonic oscillator exactly match the classical limit? Background ...
0
votes
2answers
157 views

meaning of “sufficiently small” in approximations to behaviour of a Harmonic Oscillator

So in my classical mechanics book it states: "For any sufficiently small displacement, any system of this kind behaves like a harmonic oscillator." When discussing SHO. So I am curious what is ...
5
votes
1answer
118 views

Why is energy in a system typically able to be described using quadratic expressions?

This might be more of an applied math question. Why is the energy of a system typically able to be described using quadratic expressions. Is there an underlying mechanic that drives this?
2
votes
1answer
277 views

Why do materials obey Hooke's law? [duplicate]

Why do materials extend proportionally to the force exerted on them (Hooke's law)? I thought that when materials are compressed or extended under force, their atoms become closer or further apart; ...
2
votes
0answers
421 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 ...

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