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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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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17 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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65 views

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

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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23 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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44 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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66 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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23 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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38 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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36 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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57 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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37 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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41 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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47 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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33 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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42 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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24 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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53 views

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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55 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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58 views

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 $\mu$?
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69 views

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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63 views

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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16 views

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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26 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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23 views

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 ...
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50 views

Sign of matter Lagrangian term in curved space

In field theory the (matter) Lagrangian $\mathcal{L}_m$ is uncertain upto an overall constant multiplying factor (i.e. $\mathcal{L}_m$ and $a\mathcal{L}_m$ yield the same field equation(s) on ...
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66 views

Why is charge of the electron negative?

How did scientists figure out that the charge of the electron was indeed negative? I know how the cathode ray tube experiment works, but how did Thompson know that the plate that the cathode ray beam ...
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23 views

FRW Metric maximally symmetric, derivation, $R=3K$ or $R=6K$ confusion, two different texts

I'm looking at Tod and Hughston Introduction to GR and writing the metric in the two forms; [1]$$ ds^{2}=dt^{2}-R^{2}(t)(\frac{dr^{2}}{1-kr^{2}}+r^{2}(d\theta^{2}+sin^{2}\theta d\phi^{2})) $$ [2] $$ ...
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50 views

Direction of electric field lines and electrostatic force

Direction of electric field and electrostatic force should be same by the equation $$\vec{F} = \frac{k q q_0}{r^2}$$ Electric Field $$\vec{E} = \frac{k q}{r^2}$$ Let us suppose that there is a ...
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109 views

Why is there a negative sign in front of the optical wave?

In undergrad I lost (a lot) of marks in my optics class for writing: $$A(t) = \exp(i(\omega t + \phi))$$ Instead of: $$A(t) = \exp(i(-\omega t + \phi))$$ In a derivation where I must have needed ...
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143 views

Why does the density matrix $\rho$ obey a wrong-signed Heisenberg equation of motion?

The density matrix is defined as $$ \rho_\psi ~:=~ \frac{\lvert\psi(t)\rangle \langle \psi(t)\vert}{ \langle \psi(t) |\psi(t)\rangle }$$ in the Schrödinger picture. $\rho_\psi$ is obviously a time ...
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29 views

Limits of Integration Trig, Mag Field Infinite Length Wire

I don't understand how the limits of integration should be defined when doing basic integrals of trig functions. It seems like it's an arbitrary decision, I don't understand it. Here's the set up: ...
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51 views

Why am I getting that work it's always the same in both directions?

I'm studying electrostatic and I'm getting pretty frustrated because with the definition of work I'm getting that it's always positive and it doesn't make any sense. So here I have 2 positive ...
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71 views

Potential Energy in modified Atwood Machine

The initial length of the spring is $l_0$. I need help understanding how the potential energy of this system comes to be. I know the answer: $$ U = ...
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79 views

Why is the total energy of an orbiting system negative?

Assume it's an circular orbit. Object A orbits around object B. Take object B as frame of reference. .$E=KE_a + GPE$ .$E=\frac 12m_av_a^2 +(-\frac {GM_bm_A}r)$ .$E=\frac 12m_a(GM_br)+(-\frac ...
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82 views

Why “colours” of light are given in wavelength not frequency?

If I understand correctly, when a beam of (monochromatic) light passes through media of different refractive indices, its wavelength changes but frequency remains constant. Why, then, are colours of ...
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129 views

Sign convention for the Minkowski metric $\eta_{\mu\nu}$

In special relativity, one is confronted with a quadratic form called proper time, which is $c^2t^2-(x^2+y^2+z^2)$, $t$ being time and $x,y,z$ being the space coordinates. One usually introduces a ...
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37 views

Usage of singular or plural SI base units when written in both symbol as well as name [closed]

I have multiple doubts related to the usage of singular or plural SI base units when written in both symbol as well as name. I have framed this question under two parts, namely, Part (a) and Part ...
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148 views

Calculating $\langle x | \hat{x} | p \rangle$ in $p$ basis

I am trying to calculate $\langle x\ |\ \hat{x}\ |\ p\rangle$. I can work in the $x$-basis like so: $$\langle x\ |\ \hat{x}\ |\ p\rangle=\int dx'\langle x\ |\ \hat{x}\ |\ x'\rangle\langle x'\ |\ ...
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28 views

What does “Receptor” convention refers to in RC circuits?

my question is How can we choose the convention in a circuit and what does it refer to ? Especially for a Capacitor I hear the terms "passive sign convention..." "receptor convention ..." "generator ...
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28 views

Why is cap voltage negative in KVL for discharge circuit?

I was just trying to derive the equation for a capacitor discharging through a resistor, and I've run into in a problem. If I set up my KVL, then I would say $iR = V_c$ (where $i$ is instantaneous ...
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60 views

Representation Of Linear Velocity as Cross Product

Why is linear velocity represented as cross product of angular velocity of the particle and its position vector? Why not vice versa? (Consider rigid body rotation)
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27 views

Unit definition concerning light and metre [closed]

A stupid question. I see metre is officially defined based on the speed of light: The meter is the length of the path travelled by light in vacuum during a time interval of 1 / 299 792 458 of ...
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1answer
148 views

Gravity in $d$ spacetime dimensions

Given the following action $$S=\frac{1}{16\pi G}\int d^4x \sqrt {-g}(R+aR^2+bR_{\mu\nu}R^{\mu\nu}+cR_{\mu\nu\lambda\sigma}R^{\mu\nu\lambda\sigma}),$$ which is in 4D. How to we generalise this ...
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56 views

How do I represent $A$ transpose $A$ in indicial notation?

I know this question sounds lame, but the book I am following doesn't use the answer I expect and it has been using a similar notations everywhere else which has confused me. I think Q[Any tensor] ...
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35 views

Integral limits when calculating the work

If I integrate $$dW= \vec{ F} \cdot d\vec{\ell}$$ which are the limits? In $$\int\limits_{W_{inf}}^{W_{sup}}dW= \int\limits_{\vec{\ell}_{1}}^{\vec{\ell}_{2}} \vec{ F} \cdot d\vec{\ell}$$ it is ...
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53 views

Which is the right sign convention for the potential difference?

The circulation of the electric field gives the potential difference, but is it : $$V_B-V_A = \int_A^B\vec{E}.\vec{dOM} \hspace{1.5cm} (1)$$ or $$V_B-V_A = - \int_A^B\vec{E}.\vec{dOM} \hspace{1cm} ...
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69 views

Question on boundary condition for Maxwell's Equations and Coulomb's law

When deriving Coulomb's law using the differential forms of Maxwell's equation, the boundary condition that $\phi = 0 $ at infinity is also used. From $\nabla × E = 0, E = \nabla \phi$ for some ...
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51 views

Why is the imaginary unit conventionally put on the right hand side of commutation relations? [closed]

Commutation relations in quantum mechanics are usually written in the form $$ [x_i,p_j] = i \hbar \delta_{ij} $$ with the imaginary unit $i$ put on the right hand side of the equation. But ...
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36 views

Meaning the symbol, $W$ and $dW$

What's the difference between $W$ and $dW$? They are both work done and have similar formulae (same dimension). But I don't know the difference between them. $dW$ here ISN'T power.
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102 views

Why did scientists need to invent light years?

Why did scientists need to invent light years? What's so important about having a light year? I have been learning that a light year is $9.461 \times 10^{15} \, \mathrm{m}$. My question is, why are ...