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I read a paper about boundary conditions and imaginary potentials. In this paper the author considers a single, non-relativistic quantum particle of mass $m > 0$ in $1$ dimension with a soft detector in finite interval $[0,L]$, $L>0$, with Schrödinger equation
\begin{equation}
i\hbar \frac{\partial\psi}{\partial t} = -... |
Physicist Geoffrey Chew proposed the concept of bootstrap (related to S-matrix theory) where he denied that fundamental laws of nature existed at all, as it is indicated in a writing in his memory written by one of his collaborators 1:
The bootstrap philosophy abandons not only the idea of fundamental constituents o... |
Explain with the use of equations why a pistol fired from the clouds 10km away is capable of killing a person on the ground compared to when it is fired horizontally over same distance.
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And if this is the case, what is the reason that the re-emitted photon (when the electron moves from an orbit to a further orbit) has a different wavelength than its wavelength when it was received?
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I've tried to understand the decomposition of an HF electrical field in a series of plane waves.
$$\vec{E}(\vec{r}, t) = \int\int\int \hat{\vec{E}}(\vec{k}) \cdot\mathrm{e}^{\mathrm{i}(\vec{k}.\vec{r}-\omega t)} \mathrm{d}^3\vec k$$
The fourier component corresponding to $\vec{k} = 0$ does not represent any plane wave.... |
According to Goethe when an observer looks through a prism at a white rectangle cast against a black background two border spectra appear (one formed by a red and yellow combination of colours, the other by a violet and blue combination) due to the fact that the prism moves the rectangle from its initial position in a ... |
The third law of Newton assumes that forces are due to the interaction of two bodies. Of course, a particle can interact with several others. But the result of these interactions can always be broken down to interactions between pairs of particles. Is there in nature an interaction, say between three bodies, whose resu... |
My biology textbook says:
The general rule is that the limit of resolution is about one half the wavelength of the radiation used to view the specimen.
This means anything smaller than half the wavelength won’t be resolved. Why exactly is this the case?
I gathered diffraction has a role to play.
From my research I ca... |
The wiki says that rotational inertia is defined for point-masses, and by extension continuous bodies. It says:
This simple formula generalizes to define moment of inertia for an arbitrarily shaped body as the sum of all the elemental point masses $dm$ each multiplied by the square of its perpendicular distance $r$ to... |
I am reading a research paper and to explain an experimental data, the author has written....
The 68A MeV Li + p scattering data are reanalysed.....
I understand that A = atomic mass but how do I read this?
Is it something like 68 MeV beam is used? But then why did they write A?
I am a bit new to this. Sorry if it’s a ... |
If every function of the form $f(x-vt)$, in the one dimensional case for example, solves the wave equation for a wave propagating in the positive $x$ direction, why do we always represent the solution as $f(kx-\omega t - \varphi)$? How and why would we go from the first solution to the other? In textbooks they just sea... |
Since water molecules are dipoles and get excited by microwave radiation I wonder if the opposite is true and water can act as an electromagnetic emitter.
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Or is there a bias toward a specific angle in regards to the direction of the current?
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In my research I find an equation featuring the "exponential entropy" term $\mathrm{e}^{H(p_{i})}$ and I wonder if it has a specific meaning. I have only found rare references to that term (usually in terms of dispersion or "spread of the distribution") so I'm looking for more insights. I work with natural logarithms a... |
In the chapter 'Constant gravitational field' of the book 'Classical field theory' of the authors, there is the following equation:
$$v=\dfrac{dl}{d\tau}=\dfrac{c}{\sqrt{ g_{00}}}\dfrac{dl}{dx^0}$$
Now, the term $$\dfrac{dl}{d\tau}$$ is itself a speed.
What is the difference between $v$ and $\dfrac{dl}{dx^0}?$
|
I would like to ask a very basic physics question which I am struggling to find the answer to.
What would be the impact force when an object is attached to a piece of rope and pulled to a certain height then swing down to hit a wall?
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Say we've got a charge $q$ moving in a circle. Then in many texts a current due to the charge at any point on the circle is given as $I=-q/T$. Where $T$ is the time the charge takes to complete a revolution.
To me the current should be a Dirac delta function spiking when the charge crosses a point where the current is ... |
Please realize, that I am not talking about the Maximum Kinetic energy of Photoelectrons. I understand that the Max K.E. depends upon the energy of radiation used.
But the Kinetic enrgy of most electrons is less than Max K.E. so will the average K.E. of all electrons also be unaffected on increasing Intensity of Light,... |
Page 272 of No-Nonsense Classical Mechanics sketches why paths in phase space can never intersect:
Problem: It seems to me this reasoning only implies that paths can never "strictly" intersect, in the sense that two points in phase space pass through the same point (at $t$), and then split into two distinct paths.
Q... |
Both the bodies are falling in gravity and as indicated by the picture and each body has a different mass
QUESTION-1(Direct question)
From the picture if the two masses were previously connected via a string and were left to free fall, would they have the same acceleration, or different acceleration. Explain your ans... |
Consider the quantization of the electromagnetic field. In the discrete case, given in Wikipedia, the operators $\hat{a}$ and $\hat{a}^\dagger$ are dimensionless $$[\hat{a}]=[\hat{a}^\dagger] = 1,$$ which is consistent with the commutation relation $[\hat{a},\hat{a}^\dagger]=\delta_{\vec{k},\vec{k}'}$. This is also con... |
If I push my finger onto a weighing balance and it reads 100g, then how do I calculate the force produced by my finger? Do I just use F = mg? Or is this even possible?
|
I attach a picture of the notes I am using in statistical mechanics , this is the introduction to the canonical ensemble. What I don't understand is the part highlighted in yellow, that is:
"Since we do expect that only values around $\tilde E_1$ to be
relevant, and considering that $\tilde E_1 << E$ , we can expand $Ω... |
An optical bench has $1.5$ $m$ long scale having four equal divisions in each cm. While measuring
the focal length of a convex lens, the lens is kept at $75$ $cm$ mark of the scale and the object pin
is kept at $45$ $cm$ mark. The image of the object pin on the other side of the lens overlaps with
image pin that is ke... |
Given an RLC circuit I want to model the in- and out-of-phase of the voltage across the resistor $R$ as a function of the frequency $\omega$ of the AC-supplied voltage $U = U_0 \cos(\omega)$. The RLC components are connected in series, and the inductive coil of inductance $L$ has a resistor, $R_{coil}$, connected to... |
As a footnote in page-3 of Jaan Kalda's notes on mechanics, he writes if we have a force acting over an area, then we would find total torque by integrating 'something' over the total area. I'm not sure what this 'something' is, anyways, he also writes about the effective application point of forces as
$$ d \Pi = \Pi(\... |
I sometimes mistake space-time curvature for gravitational field lines. Do geodesics in some ways represent $g$-field lines? Why is not it traditional to show $g$-field lines around a massive object in general relativity the same as we do for $E$ or $B$ field lines around an electrical charge or a magnet in electromagn... |
Lifting of degeneracies of a composite system through interactions among its constituents is a generic theme of all physical systems - from splitting of $s-$orbital energies when two hydrogen atoms are brought nearby to the frequency splitting of propagating modes in optical waveguides. Through this post I am looking f... |
I was brushing off my rotational mechanics when I thought of this hypothetical scenario. The wheel has a mass m and is supposed to climb up the step by the application of some horizontal force at S. Given that the point of contact acts at a fixed axis to rotate about (there is enough friction to prevent slipping), will... |
While reading a wikipedia article about collision using reduced mass I came across this.
how has it been derived?
|
I'm reading Arnold's mathematical methods of classical mechanics and in the section he talks about newton's equation ($\ddot{\boldsymbol{x}}=\boldsymbol{F}(\boldsymbol{x}, \boldsymbol{\dot{x}},t)$) he says that this is invariant under Galilean transformations.
Right, I understand this, but now i wanna show mathematical... |
I have a question about this equation: $$\frac{1}{2}\otimes\frac{1}{2}=1\oplus0.$$
I'm a bit confused by the right-hand side. Should '1' and '0' be interpreted as the total spin? If so, if there're two particles both have spin $-\frac{1}{2}$, why there's no -1 on the right-hand side? Could '1' and '0' be treated like t... |
When dealing with s-wave scattering in ultracold atoms physics people usually work with the pseudopotential $U = g_0 \delta^{(3)}(r)\frac{\partial}{\partial r}(r\cdot)$.
On the other hand one (sometimes) uses a "bare" contact potential $U = g \delta^{(3)}(r)$ and then goes on and renormalises the coupling constant as $... |
It seems half the time I'm just guessing whether it's series or parallel, is there not a way to definitively determine whether a given connection is series or parallel just by looking at it?
|
I get that in the Schrödinger picture the wave function evolve in time and the quantum operators are independent of time. However, in the Heisenberg picture the operators evolve in time and the wave functions remain independent. I understand that the operator must obey the commutator equation but, what does it mean to ... |
I'm studying the Nishinaka-Yoshida crystal models that encode the generating function of $D4$-$D2$-$D0$ BPS bound states on a Calabi-Yau divisor.
The case of conifold at its singular point is developed in Statistical model and BPS D4-D2-D0 counting and the case $A_{N-1} \times \mathbb{C}$ is discussed in A note on stat... |
After spending some time with LQG books and articles i have still some problems regarding concepts of this theory.
Spin network is built from lines labeled by spin label $j$ and since angular momentum must be conserved at the node one needs to associate intertwiner with the node. What's the role of the Clebsch-Gordan c... |
This question, unlike potential duplicates, does not concern nonclassical theories such as general relativity or the standard model.
Many sources found by a simple google search say that there is a common misconception that gravity is force. Instead, weight is a force caused by gravity. Gravity is a phenomena that caus... |
The distance between two light rays changes as they pass from one material to another. I want to know the magnification defined as d2/d1 in terms of the angles theta1 and theta2. So far I am not able to relate d of both rays to refracted angles. Can someone guide please!
|
I am wondering if the free electrons within a straight copper wire could be compressed towards the center of the wire with the use of two electric fields created by two sets of parallel plates.
I believe that the free electrons within the wire can be compressed to a certain extent before the Coulomb force between the f... |
Alright, so now I understand that entropy is a state function and we can easily calculate it by devising a reversible path between the two states of an irreversible path. For calculating the entropy of mixing of two different gases, the professor in this video at 35:02 states that we can achieve such a reversible proce... |
I am considering phase space of configuration variables in general scalar tensor theory $(q^A=(h_{ab},\phi))$, characterised by the metric:
$ M_{AB}=\frac{\sqrt{h}}{N}\begin{pmatrix} \frac{U(\phi)}{2}G^{abcd}&-U'(\phi)h^{ab}\\-U'(\phi)h^{cd}&G(\phi)\end{pmatrix};
$
prime denotes derivative w.r.t scalar field $\phi$) ... |
I see there are many theories about transportation i.e. Einstein Debye, Boltzmann transportation theory, Landauer approach, Kubo formulas, Kyldesh/Green function formalism.
I am looking for an introductory book/article that explains these theories chronologically. I know, Kyldesh/Green functions are in itself are big t... |
Degrees of freedom of a massless rod, moving freely in space with a speck which is constrained to move on it?
It seems massless rod is ideal
I am very confused how to regulate degrees of freedom. However, I know Degrees of freedom mean minimum number of coordinate to specify something.
Any help will be appreciated.
Tha... |
There are at least two parts in this question. First one is does the interior of the ice produce radiation when it is accelerated? I guess it does not "because it is electrically neutral". But really, why not? I thought only the magnetic field is divergence-free. Second part is about the sides of the ice exposed to the... |
I think electrically neutral materials do not generate electromagnetic radiation/photons when accelerated, but I might be wrong. If I am correct though, why is it that accelerated ions generate electromagnetic radiation but not electrically neutral stuff? Do their electrical fields cancel each other (like a positive pr... |
My understanding from careful study of Bells theorem is that there may be a deep subtlety that is not ruled out, but is probably very minimally studied in the literature. However the literature is vast, and ruling out that it is not studied at all seems questionable verging on unlikely.
suppose that the hidden variab... |
The two-dimensional Anderson model is the model $$ H = T + \lambda V_\omega $$ where $T$ is nearest-neighbor hopping on $\mathbb{Z}^2$ and $V_\omega$ is a random potential. $\lambda > 0$ is the disorder strength. Taking the normalization of $T$ so that the spectrum of it is $[0,8]$, it is conjectured (yet not proven if... |
In this paper,section 3.2, Craps, Sethi and Verlinde claim that DLCQ matrix theory is valid near the big bang if
The open string oscillators decouple and
Gravity decouples from the matrix description
then proceeds to derive conditions for the validity of Matrix theory
Why do these conditions ensure the validity of DL... |
When deriving the one and two-loop result for the effective potential between two scattering supergravitons, for example from here, we see that it is always a velocity dependent potential. Supersymmetric cancellations between bosonic and fermionic oscillators ensure that no static potential exists between supergraviton... |
A follow-up question of $\frac{1}{2}\otimes\frac{1}{2}=0⊕1 $ :
If I have 4 spin-1/2 particles in my system, how can I use a series of direct sums to represent $\frac{1}{2}\otimes\frac{1}{2}\otimes\frac{1}{2}\otimes\frac{1}{2}$ ? How to determine how many singlets, total spin 1 (I think that's 3), and total spin 2s are... |
Apologies if this is the wrong Stackexchange. All the laser-cutting searches led to graphicdesign.stackexchange.com. ?!?!?!?
I have access to a laser cutting rig, a 200W CO2 beast, that needs to do a bit of an unusual job - cut something underwater. We're not looking to have the hardware submerged, but we'd like to ch... |
Space.com is not the right place to read about fundamental physics, but nonetheless I just saw Pioneering gravity research snags $3 million physics Breakthrough Prize which says:
Measurements by Adelberger, Gundlach, Heckel and their colleagues recently showed that the inverse square law holds even for objects separat... |
I just read "Newton's law of gravity says that the gravitational attraction of a star is exactly one quarter that of a similar star at half the distance" and this sentence doesn't make sense to me. Shouldn't the gravitational force be increased by 4 times when the distance is halved?
|
When Albert Einstein proposed his famous equation $E=mc^2$ for rest mass he never said anything it's about about breaking the nucleus. Then how did scientists come to know what this mean?
But again mass is not only about the nucleus. There are electrons and protons made up of quarks. Shouldn't that protons and neutrons... |
In optical fibres we reflect light by the use of total internal reflection (TIR). I know there will be some energy loss in optical fibres if we use mirrors but why there isn't significant loss in TIR? (some light must be absorbed)
|
It is stated in Sterile Neutrinos as Dark Matter that in the HDM model: $$\frac{\mu^2}{m_s}= 92 h^2 \text{eV} \tag{1}$$
where $m_s$ represents the mass of sterile neutrinos and $\mu^2$ represents the Dirac mass.
I'm also told that: $$\frac{m_\nu}{\Omega_\nu} \approx 92 h^2 \text{eV} \tag{2}$$
this is based on the HDM m... |
I am having trouble understanding how to apply the Lorentz transformation to a particle trajectory.
Suppose we have a body moving in one dimension in one frame where the position is given by $x(t) = f(t)$. Then if we apply a Lorentz transformation with velocity $v$ in the $\hat x$ direction, the trajectory in the boost... |
I am asking this regarding blackbody radiation. Water is not black, obviously. I read it is very lightly blue, but it is mostly transparent in liquid form so it probably does not absorb much of the visible spectrum nor emit anything at least at low temperatures. In solid or gazeous form it is mostly transparent too. Ho... |
If I have a hamiltonian like $\omega\sigma_z$ and 2 Lindblad operators as $\gamma\sigma_-$ and $\gamma\sigma_+$ how can I find eigenvalues of generators?
I think I should put the general form of $\rho$ and these parameters in the Lindblad equation and find $\dot{\rho}$ and then write it like
$$\dot{\rho}=L[\rho]$$
|
The system is in equilibrium, and the following discussion occurs after spring-1 is cut.
Now, as soon as spring-1 is cut it is clear that the spring force acting one M due to spring-1,will be zero instantly. Now it is said that as the two masses 2M and M are connected via a string, due to which, they will both have th... |
A car, train or a spacecraft feels a certain drag when moving through the atmosphere. I think that rolling bodies produce less drag, and hence, my question is why rolling bodies as little spheres or cylinders are not placed on the vehicle surface to reduce resistive forces. Is it that they produce more friction? why/ w... |
I understand that how helicopter hovers at the same position or a thrown ball falls to the same position even though earth is spinning. This is due to the preservation of angular momentum and my understanding is that as earth is spinning so does every thing residing on it; when a helicopter/ball leaves the surface of e... |
I was reading this paper1, which says in Eqn(15) that the derivative of a unitary gate with respect to the parameter $\mu$ can be decomposed into linear combinations of unitary gates.
However, I didn't understand how to determine the coefficient, $\alpha$ in there.
I want to implement a derivative operation in a quantu... |
I have a question concerning the time ordering operator. Let's suppose we have a time evolution generated by some Hamiltonian $H(t)$ given by
$$
U(t)=T_\leftarrow\exp\left(-\mathrm{i}\int_0^t\mathrm{d}s\,H(s)\right)\tag{1}.
$$
In Breuer and Petruccione, it's said that if the commutator of the Hamiltonian at some time $... |
What is the formal definition of trace of an operator? Suppose I have an operator $L^{a_1a_2..}_{b_1b_2..}(x,y)$ in which $a_i$'s and $b_i$'s are discrete indices, and $x,y$ are continuous ones. So how can I trace this operator? Continuous indices appear in path integral frequently.
|
This is actually a biology question, but it has to do with frame rates, so I posted it here.
Suppose, that you are looking at the lightbulb. Most of the lightbulbs nowadays run on alternating current, let's say on $50\ Hz$. When you look directly at the lightbulb, you see a steady intensity because frame rate of the ey... |
I am stuck in the way this textbook shows how Planck arrived in the conclusion that the energy of a particle must be discrete. I have done the following, assuming that the energy $\Delta E$ is discrete, we cannot integrate it, thus we use the sum as it follows.
$$
\langle E \rangle = \frac{\sum^{\infty}_{n =0}n\cdot \D... |
I'm struggling in Arnold's mathematical methods of classical mechanics when he's talking about the covariance of Newton's equation under galilean transformations (Newton's equation is $\boldsymbol{\ddot{x}}=\boldsymbol{F}(\boldsymbol{x}, \boldsymbol{\dot{x}},t)$). Here is an image of the relevant part
I don't see how ... |
When two obects $A$ and $B$ exchange heat irreversibly ($T_A\neq T_B$), the entropy of $A+B$ increases. My question is where: in $A$, in $B$, on the boundary? Is there some entropy exchange between $A$ and $B$? For the moment, my question is not really clear. I'm going to try to give a better example.
Consider a one-di... |
This is a projectile motion question and the question basically states that an object is launched at $45$ degrees with an initial velocity of $28m/s$ east.
So, how many forces are acting on a projectile when it is passing through the highest point in the trajectory if air resistance is ignored?
According to my textbook... |
If I'm carrying a bucket of water in one hand and a piece of plastic in the other, and then I decide to keep the plastic in the bucket of water (it floats). Will it feel less heavy in the second case?
I think it will feel the same because it's mass adds up to the bucket's mass and will be pulled by gravity with the sam... |
Ohm's law state that the ratio of V and I gives us a constant value of R provided that the temperature is kept constant throughout. However, in accordance with the joule's heating it would get heated by Isquare. R. So, even if the I and V remains in a linear slope of the graph, should it be rendered as ohms law since t... |
Are there any examples of conformal field theories in 3 or more dimensions that are not free or supersymmetric and can be described by a Lagrangian?
|
Recall that thermal energy is an internal energy that consists of the
kinetic and potential energies associated with the random motions of
the atoms, molecules, and other microscopic bodies within an object.)
I thought internal energy $Q-W$ depends only on temperature (ignoring phase changes) and that the potential e... |
Consider an ideal gas inside a cylinder-piston setting. Now, we know that the temperature of the system reduces under adiabatic expansion.
For an ideal gas we know that the molecules move about separately possessing kinetic energy without having any potential energy between them.
One way I think to intuitively understa... |
Whenever you see anomalous Hall effect resistivity/conductivity vs. external magnetic field curves, there is always some low-field part with a greater slope that changes to a lesser slope at some characteristic field. In magnets, this low-field region is usually attributed to magnetic domains aligning to the direction ... |
Consider an inertial system $\mathcal{O}$ and a Lorentz boosted system $\mathcal{O}'$, moving with a velocity $\vec{v}$ with respect to $\mathcal{O}$. Then we have expressions for the electromagnetic fields as follows:
$$\vec{B}=\gamma\vec{B'}+\frac{\vec{v}}{v^2}(\vec{v}\cdot\vec{B'})(1-\gamma)+\gamma\frac{\vec{v}}{c}\... |
It seems to me that the notion of 'length' (in 1 spatial dimension, I define the length of a body in a certain referential to be the maximal spatial gap of two of its points at the same time) has no analogue in time. That is, we don't have a name for the time that flow at a single point of space. So actually spatial co... |
I having trouble understanding the constraint derivative in the highlighted part of the picture below, which allows to convert the one adimensional thermodynamical relation into its dimensional counterpart.
Specifically ,when doing the derivative of the product, done with $\beta P = const$ ,why do the three derivates t... |
I get that negative values to cancel positive values, and that is the reason why we don't do a direct average. So why don't we just use the absolute value mean of the speed?
If I have one gas particle moving at $5m/s$ and one moving at $-3m/s$, yes, the average of those gives $1m/s$, sure, so why don't we just make $3$... |
I am curious to read exact solution of Helium atom in 3D. Can anyone refer me a reference, a book or a site?
|
I was interested in watching how dominos fall as part of a hugh series of them arranged that the effect can be transferred. Very simmilar is the Newton cradle where objects that are strictly localised can transfer momentum. Can a photon be something not quite identical but simmilar?Is it likely to think so if we know t... |
In anisotropic media, for extraordinary wave, I don't understand how can the power flow not be in the same direction as the propagation. I can't find a physical intuition for it.
|
Recently,my professor told me that for a qudit system we can consider the generalized $\hat{\sigma}_{z}$ observable as
$$\hat{Z}=\sum_{k=0}^{d-1}\omega^{k}|k><k|,$$
where $\omega=e^{\frac{2i\pi}{d}}$. This makes the eigenvalues complex number, however as I know that for Hermitian observable eigenvalues are always real ... |
I have a doubt that when the initial velocity given to a mass connected to a light rod fixed at one point, is $\sqrt{4gr}$ (given at the lowest point) then does it complete a circle or just reach the top and stop?
Also what will be the case of it was travelling in tube with just a little thickness so that the mass ca... |
I am these notes by Jeff Asaf Dror on Supersymmetry. In the section on the MSSM, it is stated that the most general renormalisable superpotential is given by
$$W=y_1QH_2\bar{u}^c+y_2QH_1\bar{d}^c+y_3LH_1\bar{e}^c+\mu H_1H_2 + W_{BL} \;\;\;\;\;\;\;\;\;(9.4)$$
where
$$W_{BL}=\lambda_1LL\bar{e}^c+\lambda_2 LQ\bar{d}^c+\la... |
Suppose we have an initially charged parallel plate capacitor, then we separate the plates so each plate has a positive and negative charge (I did an experiment, the plates hold the charge), I think that if the plates separately have a sufficiently high charge it could explode I am right? If that is the case, how can I... |
In a damped oscillator, the damping term is represented by a velocity dependent force $b \ \dot{x}$. This makes sense if the damping is due to viscosity of the medium.
Is this modeling correct for the energy dissipation due to heating of the spring? I understand that this heating also comes from friction but I can't vi... |
I understand that semiconductor can be either n-type or p-type (or intrinsic in the absence of doping), but what does it mean for metals to be n-type or p-type? For example, Cu and Ag are a p-type metal, and Zn is an n-type metal. What makes them n-type or p-type?
|
I cannot understand the physics behind the reflection and polarization-reflection on an atomic scale. What exactly happens at the boundary of two surfaces?
I was studying Brewster's law and thus this doubt came.
|
From a calculus-point of view, indicating what variables are constant in a partial derivative is implicit in the definition of partial derivatives. In calculus when we perform partial derivaties of functions of several variables, we don't need to indicate the other variables are being held constant, we know that is ... |
I have a system whose entropy is specified by three variables: Salinity $S$, pressure$p$, and density$\rho$.
I have the following partial derivative:
\begin{equation}
(\frac{\partial\eta}{\partial p})_{\rho,S}= -(\frac{\partial\eta}{\partial \rho})_{p,S}(\frac{\partial\rho}{\partial p})_{n,S}
\end{equation}
Where $\e... |
We know that an adiabatic expansion of a P-V system leads to reduction of temperature. Can this method be employed to continually reduce the temperature until we have exhausted the systems complete internal energy and thus attaining absolute zero temperature? Where is the caveat here?
|
Let's say we have a nanoscale laser or led(5nm width/length/height) emitting photons(red, 650nm wavelength) in a direction parallel to its plane, then at 20nm distance in the direction of the emission there is a photodiode(light detector, 5nm width/length/height).
The question: will the photodiode absorb the light(phot... |
How can I calculate the phase shift of a square membrane which is considered as harmonic oscillator by using thermal displacement and mean phonon number?
The displacement operator in QM is
$$\langle x^2 \rangle=\frac{\hbar}{2\omega m}(2n +1)$$
$$n=\frac{k_b T}{\hbar\omega}$$
where
$m$ is the mass of the membrane,
$\ome... |
I have been told that two fermions make a boson, which I am trying to prove. Suppose we have two fermion annihilation operators $c_1$ and $c_2$ such that
$$\{c_i,c_j\} = 0 \qquad \{c_i,c_j^\dagger\} = \delta_{ij}.$$
Defining a new operator $$b := c_1c_2,$$
we have $$bb^\dagger = c_1c_2 c_2^\dagger c_1^\dagger = (1-c_1^... |
Trying to obtaining the Heisenberg EOM ( "for $\vec{\sigma}$" ) for the following Hamiltonian
$$
H = - \mu \vec{B}\cdot\vec{\sigma}
$$
where the magnetic field $\vec{B}$ is generic for now, $\vec{B}=\{B_x,B_y,B_z\}$, and $\vec{\sigma}$ is the Pauli vector (of Pauli matrices).
The Heisenberg EOM reads
$$
\frac{d}{dt} A(... |
The questions is to find a natural function of $\{E, V,\mu\}$ in thermodynamics which is causing certain conceptual issues for me with the Legendre transform.
The function that has $\{E,V, N\}$ as natural variables is the entropy which is clear since the differential form of energy can be inverted for the differential ... |
As a square meter (m$^2$) quantifies area and not length, what does a square coulomb (C$^2$) quantify?
|
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