A convention is a set of agreed, stipulated, or generally accepted norms. It typically helps common efficiency or understanding but is not required, as opposed to a strict standard or protocol.

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Schrodinger's equation with negative sign

In time dependent Schrodinger's equation as given in Schrodinger's lecture (Four Lectures on Wave mechanics, Blackie & Son, 1949, pg22) he arrives at $$\nabla^2\psi-\frac{4 \pi m ...
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General proof of formulas of geometric optics?

In most lf textbooks formulas of geometric optics like lens maker formula and base formula for that are proven (or rather verified from my point of view) by taking specific case (ray diagram) and ...
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71 views

Can the sign of metric change physics?

Consider the Lagrangian of a massless real scalar (classical field) in $\phi(\textbf{x},t)$: $$\mathcal{L}=\frac{1}{2}\partial^\mu\phi\partial_\mu\phi$$ The Hamiltonian density in two different ...
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Why is friction force negative in ice skater problem?

A 68.5 kg skater moving initially at 2.40m/s on rough horizontal ice comes to rest uniformly in 3.52s due to friction from the ice. What force does friction exert on the skater? I am not really ...
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16 views

Zero of Electric Potential Energy

When you have a positive charge and a negative charge, the line that cuts perpendicularly between their separation distance is an equipotential line of 0 volts. The math indicates that at that point, ...
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35 views

Rocket equation derivation, question about signs

My question is about signs in the derivation of the rocket equation. Considering a rocket of mass $m$, its momentum at time $t$ is $p(t)=mv$. At time $t+dt$ it ejects a quantity $dm$ so its momentum ...
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Correct way to define parity of two parafermions

I am checking the literature on parafermions and it seems that people define the parity of two parafermions to be $\gamma_{a}^{-1}\gamma_{b}$. Is this definition always valid? How does one come up ...
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83 views

Why is displacement negative during free fall?

I am confused by this question. Displacement is shortest path travelled by an object, but I had seen in my book that during free fall displacement is negative.
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66 views

Negative sign in rotation operator again

In Wikipedia's page on the rotation operator, section "In relation to the orbital angular momentum", they write $$ R(z,t) = exp((-i/h) \varphi L_z) $$ where $\varphi$ is the angle being rotated ...
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111 views

Why do we use the index of refraction for yellow light?

When we do problems with optics and refraction, we’re usually given a set of indices of refraction to work with; for example, the index of refraction in air is about 1.00, the index of refraction in ...
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44 views

Classical Mechanics — Sign of work done

It seems that work has two possible ways to decide it's sign: Whether you take the perspective of the system or the surrounding (whether you consider work done on the system as positive, or work done ...
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90 views

Field expansion in Peskin & Schroeder

Peskin and Schroeder state something which I'm not fully understanding. More specificially I think it's just phrased in a way I'm not understanding. In the Schrodinger picture we can expand the real ...
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30 views

Sign convention thermodynamics

Say a system is inside a volume $V$ with surface normal vector $n$ pointing out from the volume. Then there are force vector fields (nonconservative and conservative) depending on parameters external ...
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33 views

When to use Kelvin over Rankine and vice versa

Kelvin and Rankine are both used by scientists over Celsius and Fahrenheit to record heat, but are they both used interchangeably, dependant on the country or preference of an individual, or are there ...
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98 views

Why is the electromagnetic four-potential $A_{\mu}$ not an observable?

Why within classical field-theory the electromagnetic four-potential (usually $A_{\mu}$) not an observable? In classical mechanics we don't have problems with energy measurements and in quantum ...
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41 views

About the definition of super Hilbert Spaces

I have founded in the literature at leas two different definition of Hilbert spaces: Definition 1: A super Hilbert space is a complex super-vector space $\mathcal{H}=\mathcal{H}_0\oplus ...
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1answer
70 views

Is there a scientific term for the right-hand-(grip-)rule?

To illustrate and remember the direction of rotation around an axis defined by a vector as it happens to be in some fields of physics, one can employ the right-hand-rule: (image from here) Is ...
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74 views

Different signatures

I was working out the christoffel symbols, once where the metric that I am using has (+---) signature and another time where it has (-+++) signature because two books had different signatures and I ...
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362 views

Why is a conservative force defined as the negative gradient of a potential?

I'm learning about work in my dynamics class right now. We have defined the work on a particle due to the force field from point A to point B as the curve Integral over the force field from point A to ...
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78 views

Negative sign in rotation operator (quantum mechanics, angular momentum) [duplicate]

Schaum's Quantum Mechanics comes up with $$\exp((-i/\hbar)\cdot \theta \cdot{\hat{L}} \cdot {\overrightarrow{n}})$$ as the formula of the rotation operator. Other sources I see don't have the ...
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65 views

How are these two Riemann tensor equations equivalent?

Poisson in A Relativist's Toolkit defines the Riemann tensor as$$A_{\,;\alpha\beta}^{\mu}-A_{\,;\beta\alpha}^{\mu}=-R_{\phantom{\mu}\nu\alpha\beta}^{\mu}A^{\nu}.$$ Foster and Nightingale's A Short ...
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124 views

What is the reason we originally and still use the non-SI unit, the Jansky?

The Jansky is the unit for spectral flux density. It is defined as $$1 {\rm \ Jy} = 10^{-26} {\rm W \ m^{-2} \ Hz^{-1}}$$ in terms of Watts per square meter per Hertz. I've never quite understood ...
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Do bras and kets have dimensions?

I'm trying to understand more intuitively what bras and kets are, but some aspects of them remain a mystery to me. We usually think of $\psi (x)$ as having dimension of $[1/\sqrt{L}]$ so that ...
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114 views

Where does the Lorentz boost for a Dirac spinor come from?

I have read, that if you have a Dirac spinor \begin{equation} \psi = \begin{pmatrix} \phi_R\\ \phi_L \end{pmatrix} \end{equation} that you can apply a Lorentz boost along the $z$-direction with ...
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27 views

Work done by a gas in an expansion [duplicate]

1) Consider a gas expanding quasistatically and reversibly from $V_1$ to $V_2$ at constant temperature. I want to calculate the work done. So by convention work done by a system is a negative quantity ...
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31 views

What is the correct dual of antisymmetric tensors?

In some books I find the dual antisymmetric tensor $$\tilde{H}^{ab}=-\frac{1}{2}\epsilon^{abcd}H_{cd}$$ and other times I find it with no minus sign. How can I tell which to use? Is this like that in ...
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72 views

Density of states of 3D harmonic oscillator

for the first red box, shouldn't be $\epsilon^2 =\epsilon_{n_x}^2 +\epsilon_{n_y}^2 + \epsilon_{n_z}^2 + 2\epsilon_{n_x}\epsilon_{n_y} + 2 \epsilon_{n_x}\epsilon_{n_z} + ...
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26 views

Adjoints in occupation number representation

I am having some trouble understanding how to compute things in occupation number representation. I believe my problem is only implicitly dealt with in the notes I have read. A simple example should ...
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2answers
140 views

Cross product and the right hand rule - what is the intuition behind it? [duplicate]

I understand that by convention, the cross product is defined to be the vertical projection of vector $A$ on $B$ in the case of $A \times B$. But the vertical projection of $A$ on $B$ would still be ...
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1answer
35 views

Degrees of freedom of a point mass sliding on a rigid curved wire without friction

I am very new to the subject and am going through Structure and Interpretation of Classical Mechanics. One exercise asks to find the degrees of freedom of a number of systems, one of which is a ...
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50 views

Potential step and exponential decay?

Let us say we have a wave going from a region ($x<0$) where the potential is $U_1$ to a region ($x>0$) where the potential is $U_2$. The wave function in the second region takes the form: ...
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90 views

Sign of momentum in fermion propagator

Thinking of a process like Compton scattering, where we have an electron as a propagator, I would typically write down the propagator as $$i \frac{\not q+m}{q^2-m^2}.$$ If I were to replace the ...
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31 views

Potential of an infinitely long cylinder

Suppose I have an infinitely long cylinder with radius $R$, charged with longitudinal density $\lambda$. I want to calculate the potential outside the cylinder. The field induced by the cylinder is ...
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47 views

Sign of Gaussian surface that encloses negative charge

I can't solve a contradiction that have appeared in my head. Let's assume we have a negative charge, if we enclose it by a spherical surface and $A$ is surface of the sphere, then we will have ...
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2answers
90 views

Gravitational potential difference

in my revision guide it defines gravitational potential difference as: The gravitational potential difference is work done in moving a unit mass. It then goes on to explain the gravitational ...
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1answer
666 views

What is the difference between Right Hand Palm Rule, Fleming's Right Hand Thumb Rule and Fleming's Left Hand Thumb Rule?

I dont understand in what scenarios are the three rules applied and are any two of them similar or are they all different?
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118 views

Fleming's left hand rule

in Fleming's left hand rule is the direction of current showing the direction of the flow of electrons or the direction of positive charge?
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54 views

Gravitational field strength and potential different signs

In my revision guide the gravitational field strength is given as $g=GM/r^2$ whereas gravitational potential is $V=-GM/r$. Why does potential have a minus sign but field strength doesn't?
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51 views

Cryptic remark in physics revision guide

I am currently revising for my AP physics and I couldn't understand one of the end-of-section summary notes. It says: "Remember that the direction of magnetic field is from North to South, and that ...
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51 views

Charging a capacitor (terminals)

When a battery is connected to a conductor electrons are repelled from the end of the conductor connected to the negative terminal of the battery and flow to the end of the conductor connected to the ...
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1answer
48 views

Typo in physics book (capacitors)

I'm currently working through an AP revision guide. The section on charging a capacitor outlines the following steps: When a capacitor is connected to a battery, a current flows in the circuit until ...
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37 views

Dealing with negative work

Dumb question, I'm working with vector fields right now, and one question on here tells me to assume an object can take on three paths from a to b. (paths not listed here) for times in [0,1] Now ...
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Normalising Generators of a Lie Algebra

Ok, so I'm asking this in physics because I'm currently working through part of Srednicki's text on QFT, even though it's really a maths question. In Srednicki's chapter on non-Abelian gauge theory, ...
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62 views

Why is the zero of electric potential taken to be $r = \infty$, rather than $r = 0?$

Wouldn't it make more sense if it was taken to be zero at $r = 0$? This seems to imply that with a negative test charge at $r = 0$ from a positive point charge, $V = -\infty$, which I have trouble ...
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What is precisely the energy scale of a process?

Coupling constants run with the energy scale $\mu$. But what is exactly this energy scale. My question is, if I have a physical process, how do I compute $\mu$?
3
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1answer
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Considering $\langle \underline{q} \mid \underline{p} \rangle=\frac{1}{(2\pi\hbar)^{n/2}}e^{i\underline{q}\cdot\underline{p}/\hbar}$ [duplicate]

I have been given the following complete systems of eigenvectors $$\mathbf{Q}\mid\mathbf{q} \rangle=\mathbf{q}\mid\mathbf{q} \rangle, \quad \mathbf{P}\mid\mathbf{p} \rangle=\mathbf{p}\mid\mathbf{p} ...
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Derivation of plane wave from inner product of position ket and momentum ket

In textbooks it seems to be taken for granted that $$\langle \mathbf{r}|\mathbf{k}\rangle ~=~ \frac{1}{\sqrt{\Omega}}\exp(i\mathbf{k}\cdot\mathbf{r}).$$ I'm sure it's obvious but is there a ...
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Choosing a term's sign — a rolling body question

https://prettygoodphysics.wikispaces.com/file/view/Rollin_and_Slippin.pdf In this link's first problem, top-spin is applied to a ball that slips; while the ball moves forward, it spins clockwise. ...
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60 views

Why the electrons flow from higher potential to lower potential?

We know that every thing moves from a higher potential to lower potential. In fact we also studied in our textbooks that a charge travels from higher potential ie. Positive side to lower potential ie. ...
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How can we know that a particular charge is positive or negative?

Suppose I am provided with a positive is charged....and someone tells me to find which type of charge is present in it? Then how can we detect that the body is positively or negatively charged? Is ...