Why degeneracy increases with energy
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by Robin
16h ago
So suppose I have a bunch of particles interacting among themselves with a potential function that is arbitary (not defined). The total potential energy of the system is the sum of individual interactions. How can it be possible that as the potential enrgy of the total system increase the number of degeneracy also increases? Its related to boltzmann distribution. G(w)e^-(U/KT). Here g is the density of states. How can I be sure that the density of states is increasing if I dont know about the functional form of the interaction potential ..read more
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Stress-energy tensor of a $2text{d}$ conformal field theory
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by Kutasov
16h ago
Does stress-energy tensor of a $2\text{d}$ conformal field theory split into holomorphic and anti-holomorphic part as follows? In a conformal field theory, stress-energy tensor $$T^{\mu\nu} = \frac{1}{\sqrt{-g}} \frac{\delta S}{\delta g_{\mu\nu}}$$ is traceless as a consequence of the invariance of $S$ under a Weyl transformation $\delta g^{\mu\nu} = \epsilon g^{\mu\nu}$, i.e $$\delta S \propto T_{\mu\nu}\delta g^{\mu\nu} = \epsilon T_{\mu\nu} g^{\mu\nu} = T^\mu_\mu\rightarrow T^\mu_\mu = 0\tag{1}$$ Which implies $T_{z\bar{z}} = T_{\bar{z}z} = 0$ in complex coordinates. Assuming $T(z) = T_{zz ..read more
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Deriving the Curl of the Magnetic Field, Role of the Nabla Operator
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by gluon
16h ago
We know that the magnetic field can be written in the following way: $$\nabla_{\vec r }\times\vec B(\vec r) = \frac 1 c \nabla_{\vec r}\times\int d^3\vec r_q\ \vec j(\vec r_q)\times \frac {\vec r-\vec r_q}{|\vec r-\vec r_q|^3}$$ and, using the $BAC-CAB$ identity, the curl of this becomes: $$= \frac 1 c \int d^3\vec r_q\ \vec j(\vec r_q) (\nabla_{\vec r} \cdot \frac {\vec r-\vec r_q}{|\vec r-\vec r_q|^3})-\frac 1 c \int d^3r_q\ \frac {\vec r-\vec r_q}{|\vec r-\vec r_q|^3} (\nabla_{\vec r}\cdot \vec j(\vec r_q))$$ with the property, $\nabla_{\vec r}\cdot\frac {\vec r-\vec r_q}{|\vec r-\vec r_q ..read more
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Why is the total force equated to zero [closed]
Physics Stack Exchange - Recent Questions
by Phone
16h ago
Why is the total force taken as zero ..read more
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The partition function of a particle in a magnetic field diverges. Why?
Physics Stack Exchange - Recent Questions
by Cham
16h ago
Using the symetric gauge $\mathbf{A} = \tfrac{B}{2} (-y, x, 0)$, the stationary states wave functions of a quantum particle in a constant and homogeneous magnetic field are $$\tag{1} \psi_{n m}(r, \varphi) = a \sqrt{\frac{n!}{\pi (n + |m|)!}} \, u^{|m|} \, L_n^{|m|}(u^2) \, e^{- u^2/2} \, e^{i m \varphi}, $$ where $u = a r$, $a = \sqrt{m |\omega|/\hbar}$ and $\omega = -\, q B / 2 \tilde{m}$ (the Larmor angular frequency). The functions $L_n^k$ are the associated Laguerre polynomials. Here: $n = 0, 1, 2, \dots, \infty$ and $m = 0, \pm 1, \pm 2, \pm 3, \dots, \pm \infty$. The wave functions (1 ..read more
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Dependence of stability of nucleus on the packing fraction
Physics Stack Exchange - Recent Questions
by Shivansh Jaiswal
16h ago
How does the packing fraction of a nucleus affect the stability of the nucleus? A true and false based statement question came in a exam I gave, and it stated the statement "The stability of a nucleus is inversely proportional to its packing fraction" to be "True". Google search doesn't reveal any helpful articles, though I found one handout which stated $$ \text{Packing Fraction} = \frac{\text{Actual Isotopic Mass - Mass Number}}{\text{Mass Number}} $$ and that the more negative the packing fraction, the more stable would the nuclei be. Although the relationship with stability does make sense ..read more
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Metric of a rotating Cosmic String
Physics Stack Exchange - Recent Questions
by Bastam Tajik
16h ago
I searched on the internet superficially but I couldn't find it. Is there any reference that find the solution to Einstein's Field Equations for a rotating Cosmic String? Personally haven't got the time to do the computation for the rotating flux tube extension of a 2d vortex solution to the Higgsed-$U(1)$ Yang Mills, but that's where I would definitely start from ..read more
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Why was Electric flux defined and why the way it was?
Physics Stack Exchange - Recent Questions
by Anuj
16h ago
The wikipedia definition Electric flux is the measure of the electric field through a given surface, More formally ,The electric flux $\Phi$ through a given surface $S$ is defined to be $$ \Phi=\int_S \mathbf E\cdot\mathrm d \mathbf S. $$ Firstly ,why is there a need to define such a quantity i.e what exaclty is it measuring and in what terms? -? Is it measuring the strength of electric field per unit area ,if so ,what exactly does it mean,I take Electric field value at a point to mean force that a unit charge would experience if we were to place it at that point ,and in Electric field creat ..read more
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Reflection coefficient: Acoustics vs Mechanics
Physics Stack Exchange - Recent Questions
by Lockhart
16h ago
I recently tried to derive the reflection coefficient $R$. This is not a complicated task, however after making some literature research I found two derivations which arrive at seemingly different results: The first derivation is from Griffiths ‚Introduction to Electrodynamics‘. In chapter 9.1.4 he derives the reflection coefficient of a 1D string to be $$R=\frac{c_2–c_1}{c_1+c_2}$$ where $c_{i}=\frac{\omega_i}{k_i}$ is the wave velocity, $k$ the wave number and $\omega$ the angular frequency. The second derivation is from this webpage and refers to the transmission and reflection of sound wa ..read more
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Confusion regarding magnetic moment
Physics Stack Exchange - Recent Questions
by Cooper
16h ago
Is it possible to have a magnetic configuration without a north and a south pole? My school textbook says that it is possible, as in the case of toroid and a wire carrying current. Now, the explanation given suggests that this type of case is possible if and only if a configuration has a net zero magnetic moment, as in the above case, but not for a bag magnet or a solenoid. However, I don't understand this justification, like how the di-polarity is related to the magnetic moment. Is there a mathematical interpretation ..read more
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