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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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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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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1answer
280 views

Is the spin 1/2 rotation matrix taken to be counterclockwise?

The spin 1/2 rotation matrix around the $z$-axis I worked out to be $$ e^{i\theta S_z}=\begin{pmatrix} \exp\frac{i\theta}{2}&0\\ 0&\exp\frac{-i\theta}{2}\\ \end{pmatrix} $$ Is this taken to ...
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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

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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300 views

The definition of transpose of Lorentz transformation (as a mixed tensor)

In the appendix of the textbook of Group Theory in Physics by Wu-Ki Tung, the transpose of a matrix is defined as the following, Eq.(I.3-1) $${{A^T}_i}^j~=~{A^j}_i.$$ This is extremely confusing for ...
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97 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
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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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1answer
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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What is the direction of area vector while calculating magnetic flux?

In my textbook, as a preliminary to Faraday's law of induction, magnetic flux is defined over a closed loop as $$\Phi_B = \oint \vec{B}\cdot d\vec{A}$$ Then it draws a parallel with electric flux ...
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60 views

Why does the gravitation potential in a uniform field have negative values?

As we know the gravitational potential is the work done per unit mass in taking a point mass from zero potential (at infinity distance) to a point in a gravitational field. But why is the work ...
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1answer
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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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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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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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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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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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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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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2answers
137 views

How to accurately mark with arrows an electric circuit

As I understood, we choose to mark the current with arrows going from the plus pole to the minus pole (even though we know that in reality it is the contrary). As I'm looking at electric circuits, I ...
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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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3answers
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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Why the direction of dipole moment is from negative charge to positive charge?

An electric dipole moment is defined as $p = q\times 2d$. How to understand it physically? Why the direction of the electric dipole moment is from negative charge to positive charge?
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90 views

Electric flux of a closed surface, $\Psi = Q $ or $\Phi =\int\vec{E}\cdot d\vec{A}$

I have problem with the equation of electric flux. I use one book of fundamental physics and another book of electromagnetic engineering; the two of them give different equations for electric flux. ...
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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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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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1answer
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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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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Why is potential energy negative when orbiting in a gravitational field?

I had to do a problem, and part of it was to find the mechanical energy of satellite orbiting around mars, and I had all of the information I needed. I thought the total mechanical energy would be the ...
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Which one true in First law of thermodynamics: $Q = \Delta U \pm W = \Delta U \pm p\Delta V$ or $\Delta U= \Delta Q + \Delta W $?

Which one true in First law of thermodynamics: $Q = \Delta U \pm W = \Delta U \pm p\Delta V$? (where $\Delta U$ is change of internal energy, $W$ work made by system and $Q=cm\Delta T $ heat made ...
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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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121 views

Kinetic energy (KE) in atomic orbital

Within an atomic orbital, electrons must obviously have relative differences between points in space due to potential gradient. But there is kinetic energy as well. If we choose a particular point as ...
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4answers
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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0answers
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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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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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3answers
118 views

Electric potential energy and signs

I know that electric potential is negative near a negative charge and positive near a positive charge. But does this mean a small positive 'test' charge has a negative electric potential energy near a ...
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1answer
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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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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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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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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2answers
38 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 ...