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Can a non-inertial frame be viewed as an inertial frame?

Let's consider a non-inertial frame with an acceleration of $a$ relative to an inertial frame, if $a$ is really small and we don't need extreme accuracy, can we ignore this acceleration and treat this ...
Polaris5744's user avatar
5 votes
5 answers
4k views

Wikipedia states that the relativistic Doppler effect is the same whether it is the source or the receiver that is stationary. Can this be explained?

According to Wikipedia, the relativistic Doppler effect is simply the classical Doppler effect for a stationary source, $1-v/c$, times the relativistic time dilation, $1/\sqrt{1-v^2/c^2}$ (where v is ...
John Hobson's user avatar
2 votes
2 answers
77 views

The "small amplitude" assumption in the derivation of the wave equation for the string

I am reading about the wave equation for transverse waves in a string from the book Mathematics of wave propagation (2000) by J. Davis. On page 10, just before the derivation of the (one-dimensional) ...
DinoS's user avatar
  • 21
1 vote
1 answer
80 views

David Tong, notes on General Relativity, pg. 25

I was studying GR using David Tong's notes, which I find very compelling and easy to read. The material is explained clearly to a fault, and I would recommend anyone picking up GR to at least skim ...
Filipp's user avatar
  • 13
0 votes
1 answer
83 views

Precise relation between temperature change and physical quantities [duplicate]

I've learnt that many physical quantities like length or volume etc depend on the change in temperature and some proportionality constant as: $\Delta{L}=l\alpha\Delta{\theta}$. In our physics class, ...
ekl1pse's user avatar
  • 31
3 votes
1 answer
106 views

Adiabatic Approximation in the spin 1/2 System

I am studying the following Hamiltonian: $$H(t) = \begin{bmatrix} \frac{t\alpha}{2} & H_{12} \\ H_{12}^* & -\frac{t\alpha}{2} \\ \end{bmatrix}$$ I want to assume that $\...
A. Radek Martinez's user avatar
2 votes
2 answers
102 views

WKB Approximation of the Quasinormal Mode Spectrum of the Poschl-Teller (PT) Potential

In Black Hole Spectroscopy, it is well known that the Pöschl-Teller (PT) potential behaves approximately, or similarly to the more complicated Regge-Wheeler (RW) Potential. The WKB Approximation has ...
RudyJD's user avatar
  • 481
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0 answers
44 views

Is there a deeper relationship between symmetry and gravitational potential comparing Newton's and Einstein's gravity?

In this question, see Why is general relativity in (2+1) dimensions different from cylindrical systems in (3+1) dimensional GR?, it is mentioned "The gravitational potential Φ of an infinite rod ...
timm's user avatar
  • 1,589
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0 answers
69 views

Why can we use $|p| \approx\hbar /\langle x\rangle$ as an approximation?

In our lecture, the approximation for the zeeman energy shift is $$\frac{2e \vec{p} \vec{A}}{2m} \approx \frac{e \hbar B}{m}.$$ Here, symmetric gauge was used (therefore $A \approx r B$) and my ...
phein1's user avatar
  • 11
8 votes
1 answer
2k views

A better Schrödinger Equation with Relativistic Effects?

When you derive the Schrödinger Equation from the Hamiltonian, you perform the following approximation: $$ E^2 = (pc)^2 + (mc^2)^2 \; \; \; \Rightarrow \; \; \; E = \sqrt{(pc)^2 + (mc^2)^2} $$ $$ E = ...
Álvaro Rodrigo's user avatar
4 votes
1 answer
60 views

Inconsistency in transition rate derivation in "Introduction to the Quantum Theory of Scattering" by Rodberg and Thaler

I've been working through the derivation of the transition rate in the book "Introduction to the Quantum Theory of Scattering" by Leonard S. Rodberg and R. M. Thaler (Chapter 8, Section 4 &...
Frank's user avatar
  • 466
1 vote
0 answers
42 views

Einstein's equation of gravitation field [duplicate]

I'm looking for the reason why there is the number eight $8$ at the r.h.s. of EI: $$R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=\frac{8\pi G}{c^2}T_{\mu\nu}.$$ My attempt was to take the limit of this equation ...
user2925716's user avatar
1 vote
2 answers
76 views

How to understand $W=pc$ in Feynman's Lectures on physics?

Pictures below are from 34-3 of Feynman's Lectures on physics. I can't understand the red line. The $p$ is momentum, $c$ is light speed. I can't understand the red line. I feel the author think $pc$ ...
Enhao Lan's user avatar
  • 351
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0 answers
44 views

Where comes the Biot-Savart formula from? [duplicate]

I learned about the Biot-Savart Law recently. I understand how to calculate magnet fields with it, but where does this formula $$dB=...$$ come from? My professor just told me we do that in theoretical ...
jurek's user avatar
  • 1
1 vote
1 answer
63 views

Approximation of solution for Laplace's equation in 5d (Kaluza-Klein)

I apologize for the following question because it will seem like a cheap please help me with my homework one. I just want a hint as to what direction to follow. Suppose we have a 5d space where the ...
user20046481's user avatar
0 votes
0 answers
54 views

Derivation of Compton wavelength in Tong's QFT notes

On page 2 of David Tong's notes on QFT: http://www.damtp.cam.ac.uk/user/tong/qft.html, he makes use of Heisenberg's uncertainty principle to describe relativistic effects for a particle of mass $m$ in ...
ratchet411's user avatar
0 votes
2 answers
128 views

Physics And Approximations [closed]

I started learning physics this year and one of the things I noticed is there are a lot of approximations in physics, especially in the derivation of an equation. When I am solving a problem and I ...
Sam Tunkaho's user avatar
0 votes
0 answers
17 views

Describing two levels of a spin 1 triplet with zero field splitting as an effective spin 1/2

I am working with NV centers and there one can describe the groundstate triplet of the system with a Hamiltonian of the form: \begin{equation} H_e = D \hat{S_z}^2 + g \mu_B ( B_x \hat{S_x} + B_y \hat{...
mountim's user avatar
1 vote
1 answer
67 views

Can a positive charged body moving inside a positively charged hollow sphere crash into the sides?

One can use the Gauss' law, or the solid angle approach to prove that the electric potential inside a homogeneously charged hollow sphere is uniform. This implies that a positively body moving inside ...
GingerBadger's user avatar
6 votes
0 answers
86 views

Classical limits of Quantum Electrodynamics?

Quantum Electrodynamics is the theory that studies the interactions between matter and radiation (somewhat). How would one explain for example the movement of an electron in a constant electric field ...
dolefeast's user avatar
  • 170
0 votes
3 answers
170 views

When does Newtonian physics fail?

When does Newtonian physics fail? The answer by Zo the Relativist to the question How accurate is Newtonian Gravity? includes the statement: The key point is that Newtonian physics fails when, ...
Rihards Smilga's user avatar
2 votes
0 answers
23 views

Validity of approximations in the derivation of sound waves from Newton's laws

In deriving the wave equation describing the displacement of air in the atmosphere usually some assumptions about the displacement function $\chi(x,t)$ are made. For example Feynman says: Now in ...
slow thinking's user avatar
0 votes
1 answer
80 views

Is there a multi-particle version of the Pauli equation?

The Pauli equation describes a non-relativistic spin-1/2 particle in an electromagnetic field. The solution is a two-component wave function. However, what if we have a system of two particles that ...
FusRoDah's user avatar
  • 689
0 votes
0 answers
44 views

Parabolic(?) projectile orbits as an approximation to elliptical orbits given a rotating Earth

Why is projectile motion a parabola given that the Earth rotates and a parabola is an approximation to an orbit. My current thought is that projectiles don't travel in a parabola because if the Earth ...
Steven Dorsher's user avatar
3 votes
1 answer
47 views

Asymptotic form of solution to biased random walk

(Cross post from math.stackexchange) Consider a continuous time biased random walk on a 1D lattice. The random walker walks with rate $k_\mathrm{R}$ to the right and with rate $k_\mathrm{L}$ to the ...
Caesar.tcl's user avatar
2 votes
1 answer
139 views

Physical relevance of the $ij$ components of the Einstein field equations in the Newtonian limit

In the weak field limit of general relativity (with matter described by a perfect fluid consisting only of dust), we have the following correspondences: $00$-component of the Einstein field equations ...
Inzinity's user avatar
  • 830
13 votes
3 answers
2k views

Proving Kepler's second law of planetary motion using conservation of angular momentum: What about gravity from other planets?

I'm reading An Introduction to Mechanics by Kleppner and Kolenkow. In the chapter on angular momentum, a (beautiful!) example is given by discussing Kepler's second law of planetary motion. The law ...
Aviv Cohn's user avatar
  • 605
2 votes
0 answers
70 views

Sakurai's explanation of the dipole approximation

In chapter 5 of Sakurai's Modern Quantum Mechanics (3ed), he considers the dipole approximation for an electron absorbing electromagnetic radiation due to a harmonic electromagnetic potential. In the ...
Silly Goose's user avatar
  • 2,676
1 vote
1 answer
64 views

Derivative of $c(t)$ in Adiabatic Approximation

In Sakurai's Modern Quantum Mechanics, second edition, $5.6.10$ is $$\begin{aligned} \dot{c}_m(t)=-\sum_nc_n(t)e^{i[\theta_n(t)-\theta_m(t)]}\langle m;t|\left[\frac\partial{\partial t}|n;t\rangle\...
liZ's user avatar
  • 37
7 votes
1 answer
204 views

How to get the factor of $n^{-27/4}$ in number of open string states from the calculation in GSW's book?

In section 2.3.5 of Green, Schwarz, Witten's book on string theory (volume-1) pp. 116-118, the objective is to calculate an Asymptotic Formula for Level Densities $d_n$ for open bosonic string theory. ...
Sanjana's user avatar
  • 785
0 votes
5 answers
178 views

Why are we able to observe seemingly "inertial objects" in our day to day life? (apparent paradox from Newton's second law)

On the table and near to the computer where I write this question on, is my phone, and in my observation, it is completely still. Now, by Newton´s first law, since it is inertial, there is no net ...
Cathartic Encephalopathy's user avatar
2 votes
4 answers
181 views

Why the products of $\Gamma$'s of the Ricci tensor can be neglected in linearized GR?

In the linearization of GR, when $g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}$, and $|h| \ll 1$, it is said (for example here) that 'to linear order the “$\Gamma\Gamma$” terms go away' in the formula for ...
Claudio Saspinski's user avatar
3 votes
2 answers
176 views

Making sense of stationary phase method for the path integral

I am trying to understand this paper/set of notes. I have already seen the following related question: Does the stationary phase approximation equal the tree-level term? but had some trouble following ...
CBBAM's user avatar
  • 3,370
0 votes
1 answer
68 views

Taylor Approximation for Time Dilation and Lorentz Contraction

I don't know why the taylor expansion for the time dilation and lorentz contraction look like this. Here, the velocity $\mathbf v$ of $\overline{\mathit O}$ relative to $\mathit O$ is nearly that of ...
Gene's user avatar
  • 63
3 votes
0 answers
41 views

What is the relation between the Adiabatic Approximation used in quantum chemistry and the one given in QM textbooks?

I am an aspiring quantum chemist and have come across two vastly different versions of the Adiabatic Approximation when studying Quantum Mechanics from the perspective of physics and chemistry ...
Uranium238's user avatar
2 votes
2 answers
114 views

Consistency of perturbative theory when some of the first-order terms are smaller than second-order terms?

There is something that always puzzled me with perturbative approaches. To my understanding perturbative approaches are often qualified in terms of the order of the perturbation considered. For ...
Vincent's user avatar
  • 1,109
1 vote
2 answers
564 views

Can the value of Limiting friction be achieved?

My teacher states that if we apply an external force just equal to the value of limiting friction, then the body will start moving. But if the external force is just equal to the maximum frictional ...
Madhav Mittal's user avatar
5 votes
1 answer
230 views

Why and how we study different limits in quantum gravity?

While I'm reading an article, I get confused by why and how we study different limits in quantum limit. In this paper, the author introduced four limits in D0-brane quantum mechanics: the DKPS (...
Errorbar's user avatar
  • 368
3 votes
1 answer
301 views

Classical formulation of mechanics applied to Quantum Mechanics

According to Ehrenfest's theorem, the expectation values of observables such as position ($x$), momentum ($p$), etc. behave not only in a deterministic way but in fact in a classical way. Therefore, ...
Lagrangiano's user avatar
  • 1,616
3 votes
2 answers
371 views

Recover non-relativistic density of state

The density of state of a non-relativistic particle ($E = \hbar^2k^2/2m$) in 3D is: $$\rho_{class}(E) = \dfrac{V}{4\pi^2}\left(\dfrac{2m}{\hbar^2}\right)^{3/2}E^{1/2}.$$ The density of state of an ...
Syrocco's user avatar
  • 1,168
0 votes
1 answer
65 views

Special relativity velocity addition formula precision [closed]

I tested the special relativity addition formula $$u_{\text{total}}=\frac{v+u}{1+\frac{vu}{c^2}}$$ and found that addition of small numbers converges to smaller speed, but bigger numbers to bigger ...
Vadim Ostanin's user avatar
0 votes
0 answers
21 views

Approximations in computing pressure force on volume element

I'm trying to derive the formula for the value of the pressure force on an infinitesimal fluid element, with all the approximations usually thrown under the rug (at least in my textbooks) being ...
aidaGoG's user avatar
  • 13
3 votes
2 answers
84 views

What factors does a Spring depend on?

When we consider an ideal spring, the force applied by the spring is proportional to its extension $f_{sp} = kx$. Does the same apply in real life? So I took it into my own hands. I got a spring ...
Dev Not Taken's user avatar
9 votes
5 answers
2k views

Mars' orbital period

The orbital period of Mars, is, as anyone can find at Wikipedia, $T=686.98$ d, and the semi-major axis of its orbit is $a=2.2794\cdot10^{11}$ m. This gives $T=2\pi\sqrt{\dfrac{a^3}{GM}}=686.84\text{d}$...
user2425's user avatar
  • 211
3 votes
3 answers
617 views

Understanding Kirchhoff's first law in charged conductors

I wonder about Kirchhoff's first law in charged conductors. Consider: $$j = \sigma E \implies \nabla \cdot j = \sigma (\nabla \cdot E) = \frac{\sigma \rho}{\epsilon_0}$$ This means that Kirchhoff's ...
Niclas's user avatar
  • 363
3 votes
2 answers
131 views

Quantizing Wave Vectors in 2D Electron Gas: Periodic vs Hard Wall Boundary Conditions?

I'm studying the behavior of a two-dimensional electron gas in a magnetic field, focusing on the quantization of wave vectors and the resulting energy levels, specifically Landau levels. However, I've ...
RicknJerry's user avatar
1 vote
0 answers
61 views

Why Quantum Field Theory series expansion is called Asymptotic? [duplicate]

I once saw the Freeman Dyson's article, referring the Expansion series occurring in Quantum Field Theory is asymptotic in nature; It will deviate from actual physical phenomena when too many terms are ...
K.R.Park's user avatar
  • 321
2 votes
1 answer
82 views

Struggling with understanding two approximations in Statistical Physics [closed]

I am a student finishing my bachelors in Applied Physics, and whilst studying for Statistical Physics I came across 2 approximations I can't understand. These are the Quantum corrections for an Ideal ...
Im_Trying's user avatar
-1 votes
1 answer
105 views

How can I can solution to BCS gap eq. around critical point $T_c$?

The BCS gap equation is $$1=gn\int_0^{\Delta\epsilon} d\epsilon \frac{1}{\sqrt{\epsilon^2+\Delta^2}}\tanh\frac{\sqrt{\epsilon^2+\Delta^2}}{2kT}.$$ At the critical point, we have $\Delta=0$, therefore ...
st zhang's user avatar
4 votes
1 answer
484 views

Faraday's law and Kirchhoff's law

Suppose we have a closed loop in a changing magnetic field. By Faraday's law this would induce an emf in the loop. However by the Kirchhoff's law the total emf around a closed loop is zero. It seems ...
Irene's user avatar
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