Questions tagged [approximations]
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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 ...
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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) ...
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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 ...
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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, ...
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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 $\...
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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 ...
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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 ...
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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 ...
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A better Schrödinger Equation with Relativistic Effects?
When you derive the Schrödinger Equation from the Hamiltonian, you perform the following approximation:
$$
E^2 = (pc)^2 + (mc^2)^2 \; \; \; \Rightarrow \; \; \; E = \sqrt{(pc)^2 + (mc^2)^2}
$$
$$
E = ...
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Inconsistency in transition rate derivation in "Introduction to the Quantum Theory of Scattering" by Rodberg and Thaler
I've been working through the derivation of the transition rate in the book "Introduction to the Quantum Theory of Scattering" by Leonard S. Rodberg and R. M. Thaler (Chapter 8, Section 4 &...
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Einstein's equation of gravitation field [duplicate]
I'm looking for the reason why there is the number eight $8$ at the r.h.s. of EI:
$$R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=\frac{8\pi G}{c^2}T_{\mu\nu}.$$
My attempt was to take the limit of this equation ...
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How to understand $W=pc$ in Feynman's Lectures on physics?
Pictures below are from 34-3 of Feynman's Lectures on physics. I can't understand the red line.
The $p$ is momentum, $c$ is light speed. I can't understand the red line. I feel the author think $pc$ ...
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Where comes the Biot-Savart formula from? [duplicate]
I learned about the Biot-Savart Law recently. I understand how to calculate magnet fields with it, but where does this formula $$dB=...$$ come from?
My professor just told me we do that in theoretical ...
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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 ...
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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 ...
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