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In general relativity, if there is a line element of the form $$ds^2 = [f(u, v)]du^2 + [h(u, v)]dvdu + [w(u, v)]dv^2$$ which I believe corresponds to metric coefficients $$g_{00} = f(u, v)$$ $$g_{01} = \frac{1}{2}h(u, v)$$ $$g_{10} = \frac{1}{2}h(u, v)$$ $$g_{11} = w(u, v)$$ Does one have to 'guess' a coordinate trans... |
how we can observe the wave nature of a typical tennis ball. Construct a thought experiment
|
For an Intro. Thermal Physics course i am taking this year, I had a simple problem which threw me off-guard, I would appreciate some input to see where i am lacking. The problem is as follows:
Does the entropy of the substance decrease on cooling? If so, does the total
entropy decrease in such a process? Explain.
Here ... |
I understand that an RGB LED produces light in three constrained wavelength ranges and that any color beyond R, G, or B (orange, say) is due to the interaction of the cells in our eyes with the various wavelengths of light from the LED.
I am interested in building a spectrophotometer. It does not have to be highly pre... |
I have learn two form of two postulates of quantum mechanics:
First Form
The independent variables $x$ and $p$ of classical mechanics now become Hermitian operators $X$ and $P$ defined by the canonical commutator $[X,P]=i\hbar$. Dependent variable $\omega(x,p)$ are given by operator $\Omega=\omega(x\rightarrow X,p\rig... |
Where can I find a good and rigorous reference on QFT and second quantization? It seems I would also require references on Hamiltonian relativistic field theory and on distribution theory on manifold, to treat second quantization properly I suppose.
|
It is often stated that the property of spin is purely quantum mechanical and that there is no classical analog. To my mind, I would assume that this means that the classical $\hbar\rightarrow 0$ limit vanishes for any spin-observable.
However, I have been learning about spin coherent states recently (quantum states wi... |
I am having some difficulty understanding how batteries work. I don't quite understand what exactly potential difference is. My textbook says it is the work done per unit charge to move an electron, but when electrons flow through a lamp how is there a potential difference created as the electrons aren't being moved th... |
I have been having a lot of trouble with this problem.
I can’t correctly write the force equations for each box, or the free body diagram for the system and the boxes themselves.
I have been stuck for hours. If someone could help that would be really nice.
The question is here: Two identical boxes are placed on an incl... |
The hierarchy problem revolves around the fact that we don't have a way to explain why gravity is so much weaker than the other forces. It may just be a coincidence, but since physicists tend to understandably not like coincidences very much, we treat it as a "problem" and therefore look for a solution.
One of the prop... |
I've learned recently that the rotation axis of Earth (axial tilt or obliquity) oscillates between 22.1 and 24.5 degrees.
I would like to understand why does that happen.
Having a basic understanding of classical mechanics, (and very little of orbital mechanics) I would have expected that the conservation of angular mo... |
I am supposed to find the angle of response θ for a cone shaped pile of sand given that the friction between the sand granulas is μ.
This is easily calculated as $θ = \tan(μ)$ with the help of a free-body diagram showing your common "body on an inclined plane" figure.
However, it gets complicated for me when I am suppo... |
In non-relativistic quantum mechanics, in position space, the complex conjugate operator $C$ flips the sign of the momentum operator, $CpC=-p$ (and thus also flips the sign of the orbital angular momentum).
The operator $T=C$ is usually called the time reversal operator, but this only works in certain cases. For exampl... |
So Photon has a zero restmass. And Photon can never be at rest. What does this suppose to mean? Additionally, We know that photon carries energy so Why doesn't have mass? Mass and energy are the same things to some extent.
|
The usual way to calculate how chaotic a system is would be to measure the divergence rate using the Maximal Lyapunov exponent, but it requires you to wait until infinity, measure the divergence, then calculate the exponent. Isn't that impossible?
For a system like the double pendulum, we know that two double pendulums... |
There is famous No-hair theorem:
The no-hair theorem states that all black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum.
B... |
This may be a simple question to most of you, but I'm having trouble understanding the concept behind the use of an inverting amplifier.
What is the purpose of using an op amp in an inverting amplifier if all of the current flows through the feedback resistor. In my textbook it states that the potential on the invertin... |
I was going through the question just as same below. He said to find normal reaction between 2 objects. So, why they aren't cancelling each other i.e Normal reaction of M1 on M2 and normal reaction of M2 on M1?
|
I am having trouble figuring out what is the development of the following equation due to its notation
Its a definition for the <> notation, and all that was previously stated was that $u^{(ab)} =\frac{1}{2}(u^{ab} + u^{ba}) $ is the symmetrization of the tensor $u$.
Just to be clear, my problem is with the $h^{(a}_c... |
For quite a while I've been working on the following problem:
An open cylindrical tank $2R$ meters in diameter and $H$ meters tall contains $h$ meters of water. The tank is revolved around its own vertical axis in such a way that the free surface's paraboloid touches the tanks base. How much water will be spilled?
I ... |
Given the equivalence principle, I would expect any object in freefall to have the same frame of reference, which would mean the same time dilation. I'd like to verify my understanding of this.
For example, let's say there are two space ships in orbit around a massive body, both at 5000 km. They then synchronize their ... |
I am dealing with a one-dimensional system that has a discrete translational symmetry, i.e. the Hamiltonian has the form
$$
\hat H= \frac{\hat p^2}{2m}+V(x)
$$
where $V(x+a)=V(x)$ and $\hat H$ is an operator acting on the Hilbert space $\mathcal{H}_T$.
Expressing the identity operator in the position basis one has:
$$
... |
For my introduction to quantum physics course we are using the book "University Physics volume 3", availabe here, in the linked chapter in the first paragraph of the "Using the wave function" heading, the following is stated
The energy of an individual photon depends only on the frequency of light, $\epsilon_{photon} ... |
I am writing a paper for an applied optics journal and seeking a concise reference to help dispel the following misconception about how the HUP arises in quantum optics.
At one point i cite the fundamental limit to a beam's angular spread (and therefore ability to confine it) and the beam's width, which is of course ow... |
In the paper below, on page 3, it says "In the lack of HI image, we use the r-band b/a ratio to correct for the inclination". Am I correct in thinking that what this means is that if we cannot measure the amount of neutral hydrogen in a galaxy, then measuring the amount of infrared light (in the R-band) coming from sai... |
B field at distance from the center of a ring. And the set up I built.
\begin{equation}
{B}_z = \frac{\mu _0}{2}\frac{IR^2}{(\sqrt{z^2+R^2})^{3/2}}
\end{equation}
My voltage through the large ring is 20 volts peak to peak at a frequency of 212kHz. I measure the voltage induced in my small red receiving coil. Should f... |
If I have two projectors $\pi_1, \pi_2$ such that for some $|{\phi}\rangle$:
$\langle {\phi}| I \otimes \pi_1 |{\phi}\rangle \geq e$ and $\langle {\phi}| \pi_2 \otimes I | {\phi}\rangle \geq e$
What lower bound can I conclude about the following quantity?
$\langle {\phi} | \pi_2 \otimes \pi_1 |{\phi}\rangle$
|
I was reading volume two in Landau and Lifshitz's Course of Theoretical Physics (The Classical Theory of Fields). In it, Dr. Landau develops the relativistic Lagrangian as follows: one has $$S=\alpha\int\mathrm{d}s=\int \mathrm{d}t \;L$$
where $\alpha$ is an arbitrary constant. Now, from the Minkowski metric ($\mathrm{... |
For an example, two light rays are emitted from the opposite ends of a moving train towards the midpoint, where lies a mechanism which cuts a tomato if the rays arrive simultaneously and does nothing if they don't.
For observers in the train, the tomato would be cut and the reason why would be clear. For observers at r... |
I was looking through my quantum mechanics textbook and found the following property of adjoint operators:
$$(\hat A+\hat B)^\dagger = \hat A^\dagger +\hat B^\dagger,$$
where $\hat{A}$ and $\hat{B}$ are linear operators.
How would you prove this?
|
Gauss's law for magnetism is $\vec{\nabla} \cdot \vec{B} = 0$, and I read that this implies we can write $\vec{B} = \vec{\nabla} \times \vec{A}$, for some vector potential $\vec{A}$.
I understand that having $\vec{B} = \vec{\nabla} \times \vec{A}$ implies the statement of Gauss's law. But I am having trouble proving th... |
The field forces $F_{g1}$ and $F_{g2}$ push down on Block 1 and Block 2, respectivley, where
$$F_{g1}=m_1g$$$$F_{g2}=m_2g$$
Since the pully system reverses the direction of each force, wouldn't the following be true?
$$T_1 = F_{g2} = m_2g$$$$T_2 = F_{g1} = m_1g$$
And since $m_1 \neq m_2$, wouldn't $T_1 \neq T_2$?
My t... |
I am confused about the amount of work done when lifting an object at a constant speed. If you find the work done by you on the object and the work done by gravity on the object and add them the net work would be 0. How is there an increase in Potential Energy if the net work done on the object is 0? I was told that 0 ... |
What is the physics of a bird’s forward motion?
I know that a pressure difference in the air beneath their wings and above their wings can generate an upward force called lift. The velocity of air moving over their wings can contribute to this pressure difference.
But what I do not understand is... what are the mechani... |
A uniform cylinder of mass m and radius r rolls without slipping on a parabolic surface which $y=kx^2$
then how to write cylinder’s kinetic energy by arc-length $l$. since it's not a circular surface with constant $R$， I don't know how to work out kinetic energy in this case only by arc-length.
Should arc-length be ${... |
It is common to speak of the 'wavelength' of light. For instance visible light has a wavelength of around 400 to 700 nm. A single photon can also have a wavelength, given apparently by $\lambda = \frac{hc}{E} $. My understanding is that a photon's wavelength is not related to the physical size of a photon, which is a a... |
When using Kirchhoff's circuit laws and Ohmn's law to model the system of linear equations corresponding to an electric circuit (so far, circuits involving resistors and sources only), I haven't been able to find any circuit that yields an inconsistent system nor a system with infinite solutions, thus I was wondering i... |
is it possible to safely dispose of nuclear waste by bombarding it with neutrons, and if so, what energy/temperature of neutron is required? Are thermal neutrons sufficient or must they be fast? Thanks!
|
Suppose that the state of a system of two identcial particles (say, two photons) is given by the following:
$$\frac{1}{\sqrt{}2}(|\psi_{1}\rangle|\psi_{2}\rangle + |\psi_{2}\rangle|\psi_{1}\rangle) \, ,$$
where $|\psi_{1}\rangle$ and $|\psi_2\rangle$ represent some mutually orthogonal eigenstates of an observable $\hat... |
I'm looking at the Kapitza pendulum solution on Wikipedia and am not sure how the lagrangian was simplified in one of the steps.
Using:
$$\omega = \text{frequency of base oscillations}$$
$$a = \text{amplitude of base oscillations}$$
$$l = \text{length of pendulum}$$
$$\phi = \text{angular displacement}$$
Position of p... |
If so, where does the energy come from?
|
Two blocks are placed as shown in the figure above.
Maximum possible friction between 5kg block and surface is 5 * 10 * 0.5 = 25 N (10 m/s^2 is the acceleration due to gravity).
Maximum possible friction between 10kg block and surface is 10 * 10 * 0.5 = 50 N.
The blocks are not going to move as maximum friction is 75N... |
I just recently realized - through the aid of a simple yet effective video - that mass curves not space, but spacetime. This has lead me to finally understand why we use geodesics to explain the apparent acceleration of bodies toward massive objects. My current understanding is thus that the curvature of spacetime lead... |
Two scenarios:
Solid metal cylinder of $43^\circ$ C is placed in room of $23^\circ$ C
Identical solid metal cylinder of $3^\circ$ C is placed in another (identical) room of $23^\circ$ C at the same time.
Assume heat transfer by conduction (cylinder on the ground) is negligible. Which cylinder reaches equilibrium... |
Lets say if I have a body at temperature T and the surroundings temperature is t (t>T). Does the body radiate heat to the surroundings or it just absorbs heat?
|
I live in a Class-5 night sky on the Bortle Scale, and you cannot see the Milky Way with your naked eye here. I was wondering what Class night sky I would have to be in to see the Milky Way's gas and dust clouds with my naked eye?
|
https://en.wikipedia.org/wiki/Escalator
https://en.wikipedia.org/wiki/Simple_harmonic_motion
Can we classify escalator device as a Simple Harmonic motion example?
|
I have been studying interference of light waves for a while now and I have a doubt.
I have never seen any sources (books, internet , teachers) ever take into consideration about the "actual" physical angle between Electric fields of interfering waves (or equivalently that between the Magnetic fields of interfering wav... |
Why do electrons flow from lower potential to higher potential? According to the first law of thermodynamics, energy flows from higher to lower potential spontaneously. Electrons do contain energy but why do they flow from lower to higher potential?
|
Is it true that all correlation functions of any even number of spins in the ferromagnetic Ising model with nearest neighbors interaction are nonnegative in any spatial dimension?
In the one-dimensional case, it is easy to check all correlations directly. In the general case, the positivity of all even correlations in ... |
Where I'm going wrong?
$A = \sqrt{\lambda}$, $\lambda$ is a positive real constant.
$$
<x> = \left| A \right|^2 \int_{-\infty}^{+\infty} x e^{-2 \lambda \left|x\right|}\,dx
$$
$$
= \left| \sqrt{\lambda} \right|^2 \Big\{ \int_{- \infty}^{0} x e^{2 \lambda x}\,dx + \int_{0}^{+\infty} x e^{-2 \lambda x}\,dx \Big\}
$$
$$
=... |
For a system of two completely stationary planets both of the same radius and mass, when launching a projectile (e.g. a rocket) from point A on the left planet - assuming we know U - minimal kinetic energy needed to reach the planet on the right in a straight path (launched straight towards the other 'planet'),
would ... |
Usually, the spinning chair problem is one of the typical angular momentum problems. And most of them start with a person holding two dumbbells on his two hands and bringing his arms in, then by conservation of angular momentum, the angular speed increases when he brings his arms in, and since the person is exerting fo... |
Can it be possible to form an electron-positron pair from a proton-antiproton collision through the following interaction?
$$p+\bar{p}\rightarrow[X]\rightarrow e^-+e^+$$
Where [X] is a particular unstable intermediate and will decay into electron-positron pair with few microseconds.
|
So assume we have a rod capable of rotating at its center of mass. Now we apply a force at its right edge for a very short time. Let's assume also that by the time we stop applying that force the information of a force acting has reached its center. Now, will that information continue at the left edge and tell it that ... |
We know that the heat can be converted into heat energy with the help of thermoelectric generators, but why can't we generate energy from coldness?
Like the temperature of the universe in 1 K, can this be used in the near future to be used as an energy resource for probes or satellites?
Here is the link to the article ... |
I've seen in this answer that there is an inverse relationship between the two, as illustrated by the image below. Is there any formula describing this relationship though? Thank you very much!
|
The time evolution of states under a time-dependent Hamiltonian $H_S(t)$ in the Schrödinger picture is determined by
$$
\label{TDS}
i\hbar \frac{d |{\psi(t)}\rangle}{dt} = H_{\mathrm{S}}(t) |\psi(t)\rangle,
$$
and the canonical coordinates $\mathbf{q}$, $\mathbf{p}$ are time-independent operators in this picture. Now c... |
One has that $ds^{2} = g_{ij}(x)dx^{i}dx^{j}$. I often see that the interval is re-expressed with a time "seperation" of the form:
$$
ds^{2} = g_{00}(x)dt^{2} + \tilde{g}_{ab}dx^{a}dx^{b} \;\; a,b = 1,2,3
$$
When can this be done?
Why can the proper time infinitesimal always be written in the form (according to Wiki... |
I am an IB diploma student working with the angle of refraction of water.
My goal is to note the change in the angle of refraction with temperature. However, I havent found any noticable change in my experiment. I have shined a 532 nm laser through water stored in a pot, of which I have varied the temperature from 30 t... |
Definition of work is the following:
$$W = F*d$$
$F$ is the force exerted on the direction of displacement, $d$ is the distance covered.
Let's assume net acting force on an object floating in space is $0$. This object moves with a constant velocity. Let's say the speed of object is $2 \frac{m}{s}$ for any given time $t... |
I'm continuing this question because the answer to this is not helping me. As the OP said the propagator in the problem should be given in energy basis :
$$U(t)=\sum_{\alpha=\pm}\int_0^\infty |E,\alpha\rangle\langle E,\alpha | e^{-iEt/\hbar} dE$$
But if you derive it from the expression of momentum basis :
$$U(t)=\int_... |
I opened a tin of woodstain varnish and was surprised to find that the varnish was a dark blue in colour not the mahogany which was stated on the tin.
The photograph does not do justice as to what I saw with my eyes.
The greyish/slightly mauve colour in the photograph was a darkish blue to the eye as shown by the adde... |
I have a question on the geometrical description of time-dependent quantum states and variatioanl states. I will outline my problem and ask questions along the way.
Assume you have a time-dependent state $\Psi(t) \in \mathcal{H}$ can you say that $\Psi(t)$ is a curve on a manifold parameterized with $t$?
Now we want ... |
Consider the convective term from the Navier-Stokes equation (e.g. Navier–Stokes momentum equation (conservation form) from):
$$
\nabla \cdot (\rho \vec u \otimes \vec u ).
$$
Writing the outer product for three dimensional Euclidean space:
$$
\vec u \otimes \vec u = \rho
\begin{pmatrix}
uu & vu & wu\\
uv & vv & wv... |
I have learned electromagnetic waves in a free space (conductiviy=0) propogates without loss.
But if medium have conductivity there are 2 cases good insilator case and good conductor case.
In a good insulator case it is also called low loss medium but when I look at examples if medium conductivity is low, EM waves att... |
I was told that an electron can change its position from position A to position B without appearing anywhere between A and B.
So i think that it might be possible for an electron to move in 4D or other Dimensions.
This can be further using real example. Suppose a satellite which can click photos only in 2D tries to ca... |
Recalling the statement of the problem :
Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B in the shortest time.
And as we can show with the method of variational calculus that the curve is turn out to be cycloid (Figure-A).... |
In a lattice system that exhibits quantum spin Hall effect (QSHE), like topological insulators in 2D or 3D, we call a pair of counter-propagating gapless edge states with opposite spin helical edge states, and we say that they are protected by time-reversal (TR) symmetry.
I was wondering if helical edge states can be p... |
Why is the expansion of a relativistic field into positive and negative frequency components $$\phi({\vec x},t)=\int\frac{d^3{k}}{~~(2\pi)^{3/2}}\left[A\left({\vec k}\right)e^{-i\omega_{\vec k}t}+A^*\left(-{\vec k}\right)e^{+i\omega_{\vec k}t}\right]e^{+i{\vec k}\cdot{\vec x}}$$ unambiguous in flat spacetime but not so... |
so I'm working on problem 12.60 from Griffiths EM, the goal of the problem is to find the threshold 3-momentum of a pion (as seen in the lab frame) in collision with a proton (at rest in the lab frame) so that $K$ and $\Sigma$ particles are produced. I have attached the work I've done so far on the problem, note that ... |
In Wikipedia, the Archimedes' principle is stated like this:
"The upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces"
In one section of our Physics textbook, they showed the proof of Archimedes' princip... |
I'm a theroretical computer scientist trying to get an intuition for quantum computing, and I'm
currently working through "Schrödinger's Killer App"[1] by the late Jonathan P. Dowling.
Dowling uses the analogy of quantum-entangled pocket watches carried by Alice and Bob to introduce
the reader to the concepts of nonloc... |
Question: A block of Mass m is connected to another block of mass M by a mass-less spring of spring constant k . The blocks are kept on a smooth horizontal plane and are at rest. The spring is unstretched when a constant force F starts acting on the block of mass M(horizontally) to pull it. Find the maximum extension o... |
I have some questions about some commentsthat Zee makes treating this problem in Sec II.2 of his QFT book. The Hamiltonian density of a spin-1/2 field is
$$ \mathcal{H}=\bar\psi(i\vec\gamma\cdot\vec\partial+m)\psi. $$
It follows that the Hamiltonian is
$$ H=\int\!d^3x\mathcal{H}=\int\!d^3p\,\sum_s p_0\left[ \hat b^... |
A pendulum has a mass at the point of suspension which is free to move along a horizontal line. Find:
state-space portraits, and
small amplitude solutions (analytically)
Can Anyone help me solve the following two equations
$$(M+m)l\ddot\theta+ml\dot\theta^2-ml\dot\theta=-(M+m)/g$$
$$Ml\ddot\theta+ml\dot\theta^2\... |
In all quantum mechanics books there is a formal proof that: $ (\frac{d}{dx})$ is anti-hermitian operator and thus $(i\frac{d}{dx})$ is hermitian. While proving this we also consider the fact that $[\phi ^* \psi]^{\infty}_{-\infty} =0$ .
Now what I think is that books don't write two important points explicitely:
the ... |
Consider the following configuration: A point charge sits in the upper right $(x>0,y>0,z)$ space. The other quadrants are separated by two conducting planes in the $(x=0,y,z)$ & $(x,y=0,z)$ plane. I want to calculate the work needed to create said configuration.
The electric field can be calculated using three image ch... |
I was reading the following article on wikipedia :- Wu Experiment.
The excerpt from that article is - "If a particular interaction respects parity symmetry, it means that if left and right were interchanged, the interaction would behave exactly as it did before the interchange. Another way this is expressed is to imagi... |
This question might be suited for the Electrical Engineering forum, but I think I might get more scientific explanation/discussion (rather than anecdotal) on this forum.
Is the reflection phenomenon common in RF work with unmatched source/load pairs also present at low frequencies? Or are the wavelengths so much longer... |
I'm asking this question to aid understanding of the formation of membrane potential in a cell from electrochemical gradients of ions e.g. why the membrane potential is skewed towards the equilibrium potential of K+ instead of somewhere middle between Na+ and K+ (textbooks tell you that it's because of the higher membr... |
There are a lot of questions about the double slit experiment on this site, none of them answer my question specifically, and there are basically two theories why the dark fringes should be dark:
every single photon, that is shot one at a time, lands on the bright area, thus, no photon lands in the dark area, that is ... |
I'm struggling to understand the commutator theory for quantum mechanics. I know there's the proof to do with $[P,Q]=0$ therefore there is a set of simultaneous eigenstates for $P$ and $Q$. However, if $[P,Q] \neq 0$, does it also mean that then for all $|\psi\rangle \neq 0$, we have $[P,Q]|\psi\rangle \neq 0$? Or ther... |
I know that the planetary model of an electron orbiting the nucleus is not a good way to envision it. Rather, the electron should be viewed as a cloud surrounding the nucleus.
When a photon is aimed at an atom, does the photon need to actually strike the electron exactly where it is (which would be a very small point ... |
So if a 2D aerofoil is subjected to potential flow, then there isn't a boundary layer separation at any point with the surface of the object, and hence pressure remains constant at the front and back of the aerofoil. Therefore, there is no pressure distribution and as form drag or pressure drag is caused by a pressure ... |
Recently, I came across a video on the BBC website which stated that people were 'blasting 3500 Watt lasers' at Mars.
The article (https://www.bbc.com/news/av/uk-england-hampshire-54930207) goes on about an eccentric project which includes indeed people aiming lasers at Mars, in order to 'liberate a few carbon dioxide ... |
For fermions of spin $1/2$ the angular momentum has following form:
$$
\mathcal{J}_z = \int d^{3}x \ \psi^{\dagger} (x) \left[i(- x \partial_y + y \partial_x) + i\sigma^{xy} \right] \psi(x)
$$
Here the first term is orbital part and the latter one is the spin part of angular momentum.
However, in the general prescripti... |
I was trying to read this paper http://philsci-archive.pitt.edu/3714/1/epr-bell-iep-preprint.pdf and I would like to prove the Equations (1), (2) but I am not so good for quantum mechanics so I would like your help. I understand that operator A is the orthonormal projector $$A|a+\rangle|a+\rangle=|a+\rangle|a+\rangle,\... |
Typically one assumes some sort of equilibrium to define an equation of state for a system. However, I am curious if equilibrium is actually required to define a general equation of state (with the understanding that it may not be stationary). The solar wind, for instance, is not at all in equilibrium but space plasm... |
I wanted to know if there were more than 5 states of matter (man-made or natural) and so I searched it up. Other than solid, liquid, gas, plasma, and Bose-Einstein state, these were varying results from 7 to 15 different states. I want to know what the real answer is. How many states are there and what are they? Also, ... |
I have a variable $z$ and I know its error value $\Delta z$.
So $z = 4.480$ and $\Delta z = 0.168$. I need to find $y + \Delta y$ such that
$$y + \Delta y = (z+\Delta z)^{3/2}$$
So in this case, what is $y$ and $\Delta y$?
I am finding that
$$y = z^{3/2} \tag 1$$ and $$\Delta y = \frac{3}{2} z^{1/2} \Delta z \tag 2$$
... |
When we push the wall, no work is being done. But we feel tired after some time. Since energy cannot be destroyed , the question is where does all the energy get transferred in this scenario.
Note : It cannot be all heat as we feel more tired than standing still and if it is being transferred in heat then why it is fas... |
A cannonball firing from a cannon is often given as an example of Newton's third law. The explanation goes like this: The cannon exerts a force on the cannonball and thus the cannonball exerts an equal but opposite force on the cannon. The ball accelerates rapidly and the cannon recoils in the opposite direction, but w... |
I'm trying to transform the kinetic energy Hamiltonian to momentum basis. Starting with:
$$\hat{T} = -\frac{\hbar^2}{2m}\int d^3r\ \hat{\Psi}^{\dagger}(\vec{r}) \nabla^2 \hat{\Psi}(\vec{r})$$
I can expand the field operators in terms of momentum eigenstates, since the system is translationally invariant:
$$\hat{\Psi}(\... |
A body moves in the track from A to B to C and so on. The magnitude of the velocity in any given moment is
$|\vec V|$=$t^3$$[m/s]$. The body arrives to point B at $t$$=$$2$$[s]$. The line in the draw is tangent to the track at point B and makes a $45^\circ$ with the negative x axis.
a. Calculate the tangential vector ... |
Let there be given two identical lumped element resistors $R_1=R_2$ whose heat capacities are also equal and given $C_1=C_2$. We assume the resistors are attached to thermostats, one at temperature $T_1$ and the other at temperature $T_2$ but $T_1 \ne T_2$. Now separate the resistors from their respective thermostats ... |
I see a very serious conceptual problem in the way these three equations are related to one another, as it is usually shown in electrodynamics textbooks.
Usually one starts with experimental evidence: Faraday's law of induction
The electromotive force around a closed path is equal to the negative of the time rate of c... |
Hi I'm kind of confused about the ground state degeneracy in the toric code model.
The generic ground state of the TCM is a state $|\Omega\rangle$: $A_v |\Omega \rangle = B_p | \Omega \rangle = | \Omega \rangle$
But there can be constructions of a different ground state on a torus: Suppose paths $\gamma_1, \gamma_2$ ar... |
Consider the diagram below illustrating how A-scans work, why doesn't some of the reflected sound on its way back at the red circle interface reflect again (thereby reducing the signal intensity recorded at the green arrow)?
|
I have just started studying MRI physics and was reading F.Bloch’s paper on Nuclear Induction.
https://doi.org/10.1103/PhysRev.70.460
In page 463, it is mentioned,
To obtain this variation does not require the solution of the Schroedinger equation. It is enough to remember the general fact that the quantum-mechanical ... |
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