The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [approximations]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
1answer
115 views

Taylor expansion of scalar fields [closed]

Starting of with electrodynamics I have to compute the taylor expansion around $\vec{r} = 0$ of $\psi (\vec{r}) = |\vec{r} - \vec{r_0}|^{\frac{3}{2}}$ where $\vec{r_0}$ is a constant vector up to ...
1
vote
0answers
79 views

Time-independent perturbation theory: why i'th order perturbations are orthogonal to base state?

I have been learning about time independent perturbation theory (non-degenerate for the moment), and am not satisfied about a particular point: the justification for setting $\langle n^i|n^0\rangle = ...
0
votes
2answers
128 views

Why free-fall acceleration is considered constant rather than increasing? [duplicate]

The force acting on a body of mass $m$ is $mg$, where $g$ is acceleration of free fall ! But why should there be a #uniform acceleration of free-fall in the first place? As per Newton's universal law ...
3
votes
0answers
138 views

Limitations of RPA (random phase approximation)

I'm interested in the possible limitations of the Random Phase Approximation (RPA). When is it expected to fail? As I understand it, RPA can be derived from the GW approximation, as can be seen here, ...
1
vote
1answer
43 views

Energy differentiation with cut-off function

I am a new learner of molecular dynamics (MD) simulations methods and has a simple question regarding handling of cutoff functions. In MD, pairwise energy between two atoms is assumed to be a function,...
-1
votes
1answer
85 views

How to expand this equation? $H_{1}=\frac{e^{2}}{R}+\frac{e^{2}}{R+x_{1}+x_{2}}-\frac{e^{2}}{R+x_{1}}-\frac{e^{2}}{R+x_{2}}$ [closed]

$$H_{1}=\frac{e^{2}}{R}+\frac{e^{2}}{R+x_{1}+x_{2}}-\frac{e^{2}}{R+x_{1}}-\frac{e^{2}}{R+x_{2}}$$ in the approximation $ \left |x_{1}\right |,\left |x_{2}\right |\ll R $ we expand to obtain in lowest ...
1
vote
1answer
80 views

Models in physics [closed]

As I said in another question I am just a physics enthusiast so I am sorry for my very poor knowledge. What is meant by models in physics? what is their function and why physicists imply them? Are ...
0
votes
1answer
2k views

How can I Derive the Equation for Coefficient of Linear Thermal Expansion?

I know the relationship between change in temperature and change in length. When the ambient temperature around any substance is increased, its length increases. This is due to molecules gaining more ...
-2
votes
2answers
267 views

Why does Coulomb's law hold only for two point charges? [closed]

What is the condition for validation of Coulomb's Law?
2
votes
2answers
72 views

Is the harmonic oscillator approximation valid in occasion of very powerful fields?

I noted that in physics, to study electromagnetic wave phenomena when there is a sinusoidal behaviour, often is used the approximation of harmonic oscillation. I tried to understand the basics of why ...
0
votes
1answer
104 views

Is continuum mechanics a generalization or an approximation to point particle mechanics?

Newtonian Mechanics is usually presented as a theory of point particles (and forces). My impression of the status of continuum mechanics is that it is mostly taken as an approximate description for ...
1
vote
3answers
281 views

Is the speed of light in vacuum $3\times 10^8\ \rm m/s$?

I saw another question which says the speed of light is "$3\times 10^8 \:\rm m/s$", and I know that the speed of light is $299,792,458\ \rm m/s$. My chemistry teacher taught me that $3.0$ means $3.0 \...
2
votes
1answer
107 views

Kepler's Second Law: Why do we calculate the area of a triangle rather than the area of a sector?

Kepler's Second Law states that equal areas are swept in equal times. When calculating this area, why do we use the formula for the area of a triangle rather than the area of a sector?
0
votes
2answers
366 views

Path difference in double slit experiment

Generally the path difference between two rays is considered as dsin$\theta and for this generally the two rays are considered parallel. That is shown in diagram 'c'. My questions - 1. is even ...
-2
votes
1answer
112 views

Can anyone explain the harmonic oscillator (in context to quantum mechanics) 2.3 (Griffiths) using Taylor series?

At the end he concludes $V(x) = V''(x_0)(x-x_0)^2$. How does he get to know that the rest are $0$? How does he conclude $V''(x_0) = k$. Please try to explain in easy ways and tough vocabulary. I don't ...
0
votes
3answers
65 views

Regarding assumptions

In most of the theories or derivations we take some assumptions like has is ideal, frictionless piston and many more but these are not applicable in real world. But in our real life situations we ...
2
votes
0answers
40 views

Anomalous curvature coupling corrections for $Dp$-branes worldvolume actions

The Chern-Simons term of an (abelian brane) is commonly written as $$ \sim\int_{\mathcal M_{p+1}}\sum_iC_{i}[e^{2\pi\alpha'F+B}], $$ where $C_i$ is the background Ramond-Ramond $i$-form, $F$ is the ...
1
vote
1answer
98 views

When and why are we allowed to treat a rigid body as a point mass?

When the subject Mechanics first taught, it is common that we explicitly state that the Newton's laws are valid only for point masses, and then we give examples of rigid bodies colliding with each ...
4
votes
0answers
67 views

Has anyone ever actually considered a spherical cow? [closed]

Yes, I'm aware this question is somewhat whimsical. I'm sure every physicist is familiar with "Consider a Spherical cow". Has a cow (or any animal for that matter) ever been assumed spherical for ...
-1
votes
1answer
70 views

Vacuum Conditions in teaching high school physics

I'd like to know why in high school physics is taught mostly in vacuum conditions instead of terrestrial ones. I don't mean one is more important than the other, but it's just a curiosity about that.
0
votes
2answers
86 views

Conservative $E$-field and Kirchoff rule in practice

In undergrad physics, when analyzing an LR circuit, it is often considered that Kirchoff rule holds. However, as far as I understand, Kirchoff rule only holds when E field is conservative (curl of E ...
7
votes
2answers
399 views

How can we justify, in deriving quantum statistics, the use of Stirling approximation in the form $\ln(x!)\approx x \ln x - x$?

At first sight one can say "why not to use only one term, or maybe three or more terms"? Why use two terms? I see that books (see for example good books like Griffiths quantum mechanics or Atkins ...
2
votes
1answer
197 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; ...
1
vote
0answers
143 views

Markovian approximation for teleportation? [closed]

Assume a model including a system with time dependent Hamiltonian ( 3 entangled qubits subject to a noisy reservoir) coupled weakly to a thermal bath. in order to study the time evolution of a ...
2
votes
3answers
601 views

Derivation question of WKB method

Quantum Mechanics (2nd Edition) by Bransden and Joachain contains the following passage: Substituting (8.176) into (8.171), we obtain for $S(x)$ the equation $$-\frac{i\hbar}{2m}\frac{\mathrm{d}^...
1
vote
2answers
241 views

Is there the flat Minkowski spacetime, or is it a mathematical idealization? [closed]

The occurrence of events always requires the passage of time and displacement in space. For this, we need to have a minimum of spacetime curvature. I think that the flat Minkowski spacetime doesn't ...
0
votes
1answer
106 views

How is Einstein's postulate about the invariance of the laws of physics justified? [duplicate]

According to one of Einstein's postulates related to special relativity, > "the laws of physics remain invariant in their form and nature in all inertial frames". But global inertial frames don't ...
1
vote
0answers
86 views

Is there any approximation in which the double pendulum has an exact solution?

We know that the double pendulum isn't an integrable system, since only energy is conserved versus two degrees of freedom. My question is, does a physical approximation exist, in which the total time ...
4
votes
0answers
90 views

Existence of solid mechanics problems that cannot be solved through Lax-Milgram approaches

Very often, solid mechanicians employ finite-element analyses to solve problems in linear solid mechanics. This approach is guaranteed to work because the Lax-Milgram theorem, along with some ...
2
votes
3answers
115 views

What are point objects?

I can't seem to get the idea of point mass into my head. Why are equations of physics applicable on only point masses and should be altered while dealing with object that has a collection of points? ...
2
votes
1answer
69 views

Can the jerk diverge?

In other words can the acceleration change instantly? In direction and/or magnitude. There are two aspects to this question. In a problem, can you treat acceleration as changing instantly? (when in ...
1
vote
3answers
103 views

How strict are the boundaries that divide dimensions? Is a single-layer sheet of graphene 2D or 3D? [closed]

I would like to know if there is any theory that describes a set of rules that define the boundaries of dimensions. For example, does a single layer sheet made of graphene considered a two or a three ...
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.
0
votes
1answer
101 views

Particle trapped in a double well potential and “slowly” increasing the height of the potential barrier

Today I was musing over the following problem. Consider a non-relativistic particle confined in an one-dimensional double well potential of the form $V(x)=\kappa(x^2-a^2)^2$ where both $a$ and $\kappa$...
2
votes
1answer
196 views

How can I find the metric in weak field limit for specific theory?

What is the general approach to finding a modified version of Poisson equation by means of the weak field limit of a specific gravitational theory? What is the first step? Can you introduce the main ...
5
votes
1answer
269 views

Eigenkets of degenerate perturbation theory

Suppose the original Hamiltonian is $H$ and we perturb it by a small potential $V$. The basis kets of the original hamiltonian $H$ contains some degeneracy. Since there's some degeneracy, we take ...
4
votes
1answer
93 views

Approximating sums as integrals and divergent terms

I have the following sum (notice that the sum starts from 2, i.e. there's no divergence): $$\sum_{i=2}^{N}C_i\dfrac{\exp{\left(-k| \mathbf{R}_i-\mathbf{R}_1| \right) }}{| \mathbf{R}_i-\mathbf{R}_1|}$$...
0
votes
1answer
64 views

How to deal with negative potential in the WKB approximation?

I'm trying to model a system as being inside an infinite potential well with $V(x)=-ax^v$ where $a$ and $v$ are some positive real numbers. However I'm a bit confused: if I take the - sign inside ...
11
votes
2answers
2k views

Why don't the Navier-Stokes equations simplified for hydrodynamics contain gravitational acceleration?

The incompressible Navier-Stokes equations widely used in hydrodynamics don't have the gravitational acceleration. $$ \begin{align} \frac{\partial u_i}{\partial x_i} & = 0, \\ \frac{\partial u_i}{\...
2
votes
1answer
48 views

How do you expand $\langle x'-\Delta x'\rvert \alpha\rangle$?

In my textbook (Sakurai) the following identity is often used: $$ \left< x'-\Delta x' \, \middle| \, \alpha\right>~=~\left< x' \, \middle| \, \alpha \right> - \Delta x'\frac{\partial}{\...
2
votes
1answer
109 views

In what physical situations is the weak-field limit invalid?

in the weak-field limit gravitation is described by a symmetric tensor field $h_{μν}(x)$ in flat spacetime. Linear theory suffices for nearly all experimental applications of general relativity ...
0
votes
2answers
41 views

Is there anything wrong with my Euler's method equations for a pendulum outside of small angles?

I'm trying to write a program to calculate the angle, angular speed and energy of a pendulum at different times using Euler's method. The equation I started with was:$${\rm d}^2θ/{\rm d}t^2 = - g\sin(...
2
votes
1answer
82 views

Why does mass increase when gravitational potential energy increases?

I saw a solved example in a book (Concepts of Physics by H.C. Verma, volume 2), where there is a body near surface of the earth, the problem is to calculate the increase in mass of the body when it is ...
0
votes
0answers
65 views

Derivation of rocket equation [duplicate]

Let $m$ be the mass of a rocket in free space (including fuel) at the time $t$. Now suppose that the rocket ejects a mass $\Delta m$ during the interval $\Delta t$ with velocity $v_e$ relative to the ...
2
votes
1answer
43 views

Approximating mechanical systems with high friction

I remember to have read (a long time ago) that if I have a mechanical system $\ddot x=\frac1mF(x)$ with a high friction, then I can instead study the other system $$\dot x\sim F(x)$$ to get an ...
2
votes
0answers
109 views

Validity of the thin wall approximation

Inspired by the question How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?, I decided to come back to the first paper by ...
0
votes
2answers
342 views

How the last digit in significant figures is considered doubtful?

If a reading of a length on meter rod is 44.6cm with least count of 1mm And last point of the length is exactly on 44.6 not in between of 44.6 or 44.7 Then how is it doubtful?
1
vote
1answer
196 views

Nearly circular orbits (and their angular frequency)

In 'nearly' circular motion, the radius is not constant. If the force is central the and the angular momentum is still conserved, we have a central force: where $r_0$ is equilibrium position. For ...
-4
votes
2answers
67 views

The possiblity of one more raindrops drop the ground exact same time? [closed]

Think there is a simple rain and we have got a very very sensitive clock. Is it possible to at least two raindrops hit to ground exact in same time? I mean the date time when they hit the ground, not ...
0
votes
1answer
56 views

Strong force gets weaker at small distances yet approximated by -1/r potential

My particle physics textbook (by Martin and Shaw) has confused me, it states in ch.7 that the strong force gets weaker at small distances, and that it can be approximated by $V(r) = -\frac{4 \alpha_s}{...