Questions tagged [approximations]

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4
votes
2answers
81 views

Slowly-varying envelope approximation: what does it imply?

I understand that the slowly-varying envelope approximation means that we can write an electromagnetic wave as $$ E(x,t)=V(x,t)e^{i(k_0x-\omega_0 t)},$$ where $$ \left \vert \frac{dV}{dx} \right \...
0
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2answers
82 views

How does $\sin\theta=\theta$ give a right answer even when it is an approximation?

Magnetic field at the center of circular current carrying loop is given by $$ B=\frac{\mu I}{2 R} $$ Where $\mu$ is the permeability of free space and $R$ is the radius of loop. In a question by ...
0
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0answers
78 views

Quantum numbers $n$ and $\ell$ relation in many electrons atom [duplicate]

Solving the Schrodinger equation for hydrogen atom we arrive to the conclusion that quantum numbers $n$ and $\ell$ have the relation $$\ell=0,1,...,n-1.$$ Now,since we can not solve the Schrodinger ...
4
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1answer
160 views

Coulomb's Law modified in general relativity?

It seems difficult to track down a clear explanation of this statement: So although the Coulomb law was discovered in a supporting frame, general relativity tells us that the field of such a charge ...
4
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0answers
74 views

The kinematic region for the operator product expansion

In Ch.18 of the textbook An Introduction to Quantum Field Theory by Peskin and Schroeder, on P.613 the operator product expansion (OPE) is introduced $$\mathcal{O}_1(x)\mathcal{O}_2(0)\to \sum_n C_{...
0
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1answer
117 views

Small Angle Approximation for Simple Pendulum

I am working on a simple pendulum problem. The $y$ direction is vertical and the $x$ direction is horizontal. Displacement in the $x$ direction is taken to be much less than the length of the string, ...
0
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2answers
99 views

Error of relativistic kinetic energy

I have recently begun working on the special relativity theory. I have then made the taylor series for the gamma factor to show that we get the classic formula for kinetic energy: $$E _ { k i n } = m ...
2
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1answer
131 views

Does a proton bend spacetime?

Protons have mass and as a result of einstein's field equation dictate that the spacetime is no longer flat. But yet I find in most Quantum Field Theory books the Minkowski flat spacetime metric is ...
0
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3answers
110 views

Is Stokes equation a reduction of Navier-Stokes equations?

The following Stokes problem: $$\begin{cases}-\nu\Delta u+\nabla p=f&,\textrm{in }\Omega\\ \nabla\cdot u=0&, \textrm{in } \Omega\end{cases}$$ is a reduction of the Navier--Stokes equations? ...
1
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1answer
241 views

Does Kirchhoff's Law always hold?

There's a bit of furore from this question on Youtube involving Dr. Walter Lewin and another Youtuber. With Dr. Lewin claiming Kirchhoff's Law doesn't always hold when magnetic fields are involved, ...
1
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3answers
123 views

Why we often approximate a wave function of a particle to Gaussian wave function?

I was solving problem of two particle system. We were taking wave function generally $\psi$. Later we approximated this wavefunction of two-particle system to double Gaussian wave function. My ...
0
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0answers
64 views

Taylor expansion for a double well/perturbed infinite square well

I'm trying to estimate the ground state energy for a perturbed infinite square well directly. The potential is piecewise constant $$V(x)=\begin{cases}&\infty, \qquad x<-a/2\\ &0 \qquad -a/2&...
0
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1answer
31 views

Expand the partition fct. of a simple harmonic oscillator

I come across a expansion of the partition fct. of a simple harmonic oscillator $q$ as: $$q=x^{-1}(1-\frac{x^2}{24}+...) \tag{1}$$ where $x=h\nu/kT$. It’s easy to get $$q=\frac{e^{-x/2}}{1-e^{-x}}=\...
4
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1answer
30 views

Criteria on good inertial system approximation

I'm currently wrapping my head around Newton's First Law. I think I start to get a basic understanding on the meaning of this law in terms of "the existence of inertial system". Basically my ...
1
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2answers
125 views

Series expansion of $N$-particle potential energy

I am trying to understand the so-called Taylor expansion (or series expansion) of potential energy of a system of $N$-particles. This expanded form is stated without derivation in some molecular ...
2
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1answer
54 views

How to interpret results of stationary phase approximation in GW case?

As time increases, the amplitude and frequency of the GW signal also increase. But after using the stationary phase approximation, the signal is proportional to ${1/f^{7/6}}$, where $f$ is the GW ...
2
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2answers
78 views

Capacitor demo explanation

I know that for a charged capacitor as one separates the plates further apart the voltage increases while the capacitance decreases. But surely as the plates are pulled further and further apart the ...
4
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1answer
93 views

My textbook sets $\ln \left\{ 1 + \left[ \frac{L}{L_0} - 1 \right] \right\}$ equal to $\frac{L}{L_0} - 1 $. What's the justification for this?

Sat to study physics. I started to study this new chapter Heat and Thermodynamics. It included these steps: $$ \int_{L_0}^L \frac{dL}{L} = \int_{\theta_0}^\theta \alpha d \theta; \text{ or } \ln \...
0
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1answer
37 views

What is a quasistationary approximation

I was reading an article which states : The linear-stability analysis for this system can be performed in complete generality; but it will be best for purposes of this review to go directly to ...
2
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1answer
61 views

High temperature expansion in general

I'm referencing this thesis which should be open-access. In Appendix D.1 "High temperature expansion in general", the author writes the high temperature expansion in the following way: $$ \begin{...
5
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2answers
94 views

Theoretical definition and pratical mesurement of differential cross section

In Sakurai's book, the definition of differential cross section is: $$d\sigma/d\Omega= transition \;rate / probability\; flux $$ However this def doesn't contain any information about the thickness ...
2
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3answers
78 views

Oscillator with decaying restoring force

Suppose a system that is described by the equation of motion: $$ \ddot{x} = -k\cdot x\cdot \exp\left(-\frac{t^2}{2\sigma^2}\right). $$ (For example a spring with decaying stiffness.) I'd like to ...
0
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2answers
166 views

Is the geodesic equation independent of an initial condition?

The following argument is used to determine the unknown factors (e.g., $A(r)$ and $B(r)$) in the Schwarzschild metric. $$ \lim_{r \to ∞}A(r) = \lim_{r \to ∞}B(r) = 1 \space\space\space\space\space\...
0
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2answers
36 views

Why should the spherically asymmetric part of the effective potential be small in the central field approximation?

In the central field approximation, each electron is supposed to move in an effective or average potential contributed by its attractive interaction with the nucleus and repulsive interaction with the ...
3
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1answer
246 views

What do the small terms in the series expansion of relativistic energy mean?

Through the fabulous Feynman Lectures of Physics and the introduction of relativistic mass, Richard Feynman made a link between the increase in kinetic energy of a heated molecule of gas, and its ...
6
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2answers
142 views

Composite particles Dirac spinor approximation

In many scattering process evolving composite particles such as proton, the composite particles are treated as an elementary particles. For example in electron proton scattering to the proton is ...
0
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1answer
110 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 ...
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0answers
70 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
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2answers
120 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
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0answers
109 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
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1answer
41 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
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1answer
82 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
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1answer
76 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
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1answer
1k 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
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2answers
228 views

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

What is the condition for validation of Coulomb's Law?
2
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2answers
65 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
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0answers
65 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
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3answers
252 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
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1answer
93 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
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2answers
322 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
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1answer
106 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
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3answers
64 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
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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 ...
0
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1answer
83 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
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0answers
65 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
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1answer
66 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
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2answers
74 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
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2answers
384 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
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1answer
164 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
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0answers
122 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 ...