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4
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1answer
128 views
+50

Condition for adiabatic approximation, derivation?

In quantum mechanics it is said that an adiabatic approximation is valid when $$T\gg \frac{\hbar}{\Delta E},$$ where $T$ is the time scale of variation of the Hamiltonian and $\Delta E$ is the typical ...
1
vote
1answer
49 views

The Energy Equation

I've been studying the energy equation in relativistic motion $E= \frac{mc^2}{\sqrt{1-v^2/c^2}}$, which can be expanded as $$E = mc^2 + \frac{1}{2} mv^2\text{ + some other terms.}$$ I'm curious ...
6
votes
1answer
370 views

Adiabatic approximation

The adiabatic approximation for solid state systems is rather radical. I was wondering in which cases it breaks down. As it is based on the idea of the nuclii being much heavier than the electrons I ...
2
votes
2answers
69 views

Is Huygens's Wave Theory still correct?

We have to study on details about Huygens's Wave Theory though we have Electromagnetic theory, quantum theory today. Is it still correct or not?
1
vote
3answers
70 views

Derivation of the group velocity

I know that the group velocity of a light pulse is defined as $$\begin{split}v_g&=v_p\left(1+\frac{\lambda}{n}\frac{dn}{d\lambda}\right)\\ ...
3
votes
2answers
38 views

Electric field at surface of a spherical shell

The shell theorem provides a well known result that for a spherical shell with uniformly distributed charge $Q$ and radius $R$, the electric field at a distance of $r$ from the center is: ...
1
vote
0answers
54 views

Approximate cloning of a quantum state, informed by past measurements

Suppose I give you a state $|\psi\rangle$, and tell you a sequence of measurements that have been performed on it. The measurements are not guaranteed to be orthogonal to each other, or to cover the ...
1
vote
1answer
34 views

Quick question - infinitesimals proofs [duplicate]

In a few of my courses in mechanics certain statements/equations have been proved by assuming that two infinitesimals multiplied by each other are zero. For instance in the equation : $dx + dy + dx^2 ...
0
votes
0answers
16 views

Multipole expansion of the electric field generated by an infinite charged plane

Take an infinite plate with uniform charge density, the classical problem that is usually solved with Gauss' theorem, to get that the electric field outside the plane, at a point $\boldsymbol r$ is: ...
1
vote
1answer
25 views

About field lines and continuity of magnetic and electric fields

In my laboratory class we were doing an experiment with grass seeds and iron filings to visualize the electric and magnetic field lines. So, we were discussing why they appear, because we know that ...
6
votes
3answers
912 views

Is Torricelli's law “wrong” for big holes? - Tank draining problem

Consider a tank full of water with a constant cross-sectional area A1 placed vertically on the ground. Now someone drills a hole of an area A2 in the bottom of the tank, and the liquid starts escaping ...
3
votes
1answer
89 views

Fermi's golden rule and infinite probablity?

I am slightly confused about the application of Fermi's golden rule. Which during standard derivations indicates a probability of transitioning from the state $|i \rangle$ to the state $|f\rangle$ of: ...
1
vote
0answers
30 views

Taylor expansion with fractional powers

A while ago, I was doing a physics problem, expanding to first order in a small parameter $x$, when I got an answer of $\cos^{-1}(1-x)$. This function blows up if you take a Taylor expansion, because ...
5
votes
1answer
77 views

Approximate cloning of a qubit, given multiple starting copies

Suppose I'm given several clones of a qubit in a pure unentangled state. That is to say, I'm given the state $(a \left|0\right\rangle + b \left|1\right\rangle)^{\otimes n}$. My goal is to make $d$ ...
12
votes
1answer
330 views

Could Navier-Stokes equation be derived directly from Boltzmann equation?

I know how to derive Navier-Stokes equations from Boltzmann equation in case where bulk and viscosity coefficients are set to zero. I need only multiply it on momentum and to integrate it over ...
4
votes
1answer
158 views

Solution of QM tasks by using asymptotics

When we solve QM tasks by solving the Schrödinger equation, such as tasks about a particle in a Morse potential, a Poschl-Teller potential and many others, we usually find approximations (lets call ...
3
votes
0answers
35 views

Why is stat mech involved in mean field theory?

Mean field theory involves approximating an interacting system by a non-interacting one, by replacing some operators with their expectation value. However, to my surprise, free energy is involved in ...
1
vote
2answers
74 views

Why is that a question can be answered with several theories? [closed]

This may be silly and I am sorry for that but it is confusing me. My teacher was teaching us about path of electrons around a nucleus. He told us that many theories have been proposed about path of an ...
1
vote
1answer
91 views

conservation of momentum? [closed]

At hyperphysics I got this image, with the same description in text as is in this image It says that when a massive particle (say $A$) moving with a velocity collides with an object having a ...
3
votes
1answer
170 views

Why is the Taylor expansion of the gravitational potential cut off after first term?

In this answer to a question on this site, the gravitational potential of the Earth is expanded as $$U(r) \approx U(r_0) + \left.\frac {dU(r)}{dr}\right|_{r=r_0}(r-r_0),$$ keeping only the linear ...
0
votes
0answers
50 views

Is the Fermi golden rule really accurate for calculating the life time of an atomic level?

In my impression, Fermi golden rule is routinely used in calculating the life time of an excited atomic level. But it is based on the first order perturbation theory, so it is not expected to be ...
0
votes
1answer
51 views

Am I using the variatonal method correctly conceptually?

Given A particle in a potential well: $V=-V_0 \exp(-x^2 / L^2)$ Goal Use the variational method to approximate the ground state energy My proposal The well (For $L=1$ and $V_0=10$) has the following ...
1
vote
2answers
93 views

Why can we assume, when dealing with tension, that the mass of a rope is $0$ but still assume that there are forces on it?

I started studying tension and I can't understand the following concept: If I have two objects $A,B$ collegated by a rope, where $A$ applies a certain force $\vec{F}$ on it, I would have that the ...
7
votes
2answers
247 views

Why do we still use perturbation theory, when we have advanced numerical methods and fast computers?

If my question sounds ignorant or even insulting, I apologise. I may be completely wrong, since I'm not a theoretical physicist. So, I understand why perturbation theory was originally used in ...
6
votes
0answers
116 views

Is drag force on an oscillating sphere an effective model for a swimmer?

I saw the latest video from Sixty Symbols Little Swimmers. At the end of the videos he says that we do not know how to calculate the movement of the little swimmers. He says(6:14-6:40 in video) that ...
1
vote
1answer
22 views

How to choose basis functions that contribute most efficiently per term? [closed]

I would like to approximate some positive, scalar function $f(x,y) > 0$ on a 2D field of finite size i.e. $x\in [a,b],y\in[c,d]$ I am familiar with the set of basis functions used in the Fourier ...
2
votes
0answers
60 views

Numerical problem with Hartree-Fock equations for dilute Bose gas

I have to solve the following set of equations self-consistently: $$\begin{align} n_c(\mathbf{r}) & = \frac{1}{g}\left[\mu - V_{\rm ext}(\mathbf{r}) - 2 g n_{T}(\mathbf{r}) \right] \\[3mm] ...
0
votes
1answer
46 views

Time independent perturbation theory for a 1D simple harmonic oscillator system

I have been looking through my notes and it says in a footnote that the approximation of energy levels using perturbation theory is more accurate when the energy shift of the energy levels due to the ...
0
votes
1answer
39 views

There isnt really an isolated system so why sometimes we consider a system to be isolated?

In real life, there's nothing to be called an isolated system then why at some applications do we assign isolated systems?
8
votes
4answers
814 views

Special Relativistic approximation to GR

Some time ago I was talking to a professor in college about some of the fundamental aspects and origin of General Relativity. I was surprised to learn, in fact, that a pretty good approximation to GR ...
1
vote
0answers
30 views

Approximating Gallons of Gas Needed for Trip (read: physics grad. with too much free time)

My departure from college has left me with an itch for physics-y problems to solve, and my boredom and free time gave way to this approximation of the gallons of gas I use for the trip to my ...
-1
votes
1answer
68 views

Help understanding expansion for following $\sin(\theta)$ [closed]

my professor posted a solution to a problem that I am having trouble understanding. This is the question: Find the frequency of small oscillations about the stable equilibrium position. And this is ...
2
votes
0answers
60 views

Hyperfine structure in hydrogen

Consider the Dirac equation for bounded electron in hydrogen atom. I am trying to get a clear physical explanation for all mathematical terms that appear in the Hamiltonian and energy spectrum. ...
3
votes
2answers
107 views

Any quadrupole approximation? Any example?

In atomic and molecular physics we quite often encounter with electric dipole approximation. The dipole approximation we do when the wave-length of the type of electromagnetic radiation which induces, ...
2
votes
2answers
79 views

Are some laws in physics really as simple as they seem?

For example, is $F = ma$ really an exact formula, or is it an approximation? I know a lot of formula's come from taking the first few terms of a Taylor expansion, so I was wondering if the simple ...
1
vote
1answer
140 views

How to reconcile these two approximations?

I'm working on what should be a simple problem (Taylor Classical Mechanics problem 6.23.), but I'm having a tough time reconciling the many ways it can be tackled. An aircraft whose speed is $v_0$ ...
2
votes
2answers
117 views

Why Earth is considered to be an inertial frame? [duplicate]

Earth rotates about its axis and also revolves around the Sun at the same time. So why Earth is considered as an inertial frame in Newtonian Physics. So technically, I'm effectively asking why the ...
2
votes
1answer
420 views

A missing factor of 2 in the standard Hartree-Fock mean field?

Let's start from a very simple argument: If $A$ and $B$ are some operators, then I can write their product as $$AB = (A-\langle A\rangle)(B - \langle B \rangle) + \langle A \rangle B + A \langle B ...
1
vote
0answers
44 views

The angle of a rifle to hit a target (How to make approximations to find numerical answers) [closed]

The specific question is this: A target appears at a distance of 1250m with the centre of the target 1.2m above ground level. If the sniper was firing from the prone position, the tip of the ...
3
votes
2answers
75 views

Multiple Definition For Gravitational Potential Energy?

This may just be a simple Misconception Question, here goes: Definition for Gravitational Potential Energy: The work done by gravity to pull an object to the ground. ...
0
votes
1answer
33 views

In perturbation theory, how do I determine the order of an approximation?

The title says it all: I'm confused about the various approximations and their orders. In time-independent perturbation everything is quite explicit and obvious, but, for example, how would it be with ...
0
votes
0answers
26 views

Systems with elements having size which tends to zero

[Question] If I have an element whose size(as in physical dimensions) tend to 0 but is NOT 0 (very very very small). If I create a system from these elements based on (say) the fractal concept ...
-1
votes
4answers
3k views

Are Newton's three laws of motion correct?

New technology brings new ideas with these new ideas we have to look at the old ones. Where else is a better place to start then Newton's three laws of motion! With our common age of technology do we ...
0
votes
1answer
43 views

Is “approximative reduction” general knowledge to physicists?

I came across this concept called "approximative reduction", about which there are some papers, e.g. in this collection called Structure and Approximation in Physical Theories. Very briefly, it ...
1
vote
0answers
85 views

Fresnel diffraction approximation (parabolic waves)

The Huygens-Fresnel principle (Introduction to Fourier Optics, Goodman), $$ U(x,y)=\frac{z}{i\lambda}\int_\Sigma U(\xi,\eta)\frac{e^{ikr}}{r}d\xi d\eta\,, $$ where $\cos \theta=\frac{z}{r}$, shows ...
23
votes
5answers
3k views

Is there a rigorous definition of 'much greater than'?

I have encountered $\gg$ in many physics text books where it's used as a relation between constants or functions but in none of the text books I have read is it properly defined anywhere. If $A \gg ...
0
votes
0answers
118 views

How does a ball cause a splash? (With the relevant math)

Problem Statement: Imagine a spherical ball is dropped from a height $h$, into a liquid. What is the maximum average height of the displaced water? For instance, although one particular drop of water ...
0
votes
1answer
73 views

Why is drag neglected while dealing with kinematic problems?

Why is drag neglected while dealing with kinematic problems? While dealing with problems related to finding velocity, acceleration and other kinematic problems, it is mentioned to "neglect drag". ...
2
votes
3answers
26 views

Why do we assume differential coefficients of number of molecules?

In many portions of physics (like Maxwell's velocity distribution law) we assume statements like- Number of molecules having velocity between $c$ to $c+dc$ is $dn$. But number of molecules $n$ ...