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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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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51 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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15 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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20 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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17 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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1answer
266 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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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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46 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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113 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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65 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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22 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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1answer
85 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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32 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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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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101 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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123 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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23 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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2answers
46 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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114 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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2answers
120 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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54 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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66 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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121 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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74 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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146 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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30 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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1answer
74 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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25 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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104 views

Why have they chosen this direction for current in the RC circuit? Seems pretty artificial to me

The thing is, they use this direction for current flow to derive the equation $-iR-\frac{q}{c}=0$ and then derive the equation $q(t)=Q_o e^\frac{-t}{RC}$ from the differential equation ...
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24 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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1answer
55 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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26 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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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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55 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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136 views

Can we define tension in a string as the reactive force produced in a string being pulled at both ends?

In my textbook, the definition of tension was given that Tension is the reactive force which exists when string is being stretched at its both end. After it there was a case given that to calculate ...
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83 views

Convention of tensor indices

Let $g_{ij}$ be the diagonal Minkowski metric tensor diag$(g) = (1,-1,-1,-1)$, then $g^{ij}$ is defined to be $(g^{-1})^{ij}$, hence $$g_{ik}g^{kj} = g_i^{\ \ j} = \text{diag}(1,1,1,1)=\delta_i^{\ \ ...
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1answer
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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1answer
40 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} ...
2
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1answer
64 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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4answers
306 views

Sign convention in optics

Why is the sign convention used in the derivation of the lens formula and yet used again when it is applied in numerical problems? Won't the whole idea of sign convention be eliminated if it is used ...
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2answers
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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1answer
34 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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96 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 ...
0
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1answer
38 views

Why the gravitation potential in a uniform field has 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 the point in a gravitational field. But why the work is ...
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3answers
140 views

My physics teacher gave us this equation $v= -3 +3t$

She asked us if the body was accelerating or slowing down, and I immediately said that it was accelerating (because the $a=3>0$). Then she said that I was wrong because the direction of the ...
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1answer
984 views

Sign convention for mirror and lens formulas

I have just started learning optics at school and my teacher derived the lens and mirror formulas. While doing so, she applied the sign convention for $u$, $v$ and $f$ and arrived at the final ...
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1answer
72 views

Conventional definition of ideal fluid

According to Landau&Lifshitz, an ideal fluid is one with zero viscosity and a negligible thermal conductivity. This is also the FR.wikipedia version: En mécanique des fluides, un fluide est ...
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2answers
73 views

What is the meaning of the negative sign in $W = -\Delta U$?

What is the meaning of the negative sign in $W = -\Delta U$ ? As far as I understand, $W = -\Delta U = -(U_f - U_i) = U_i - U_f$. While $U_i$ is the initial potential energy (before applying the ...
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4answers
532 views

How to indicate that a unit is dimensionless [duplicate]

For my dissertation I am preparing a list of symbols used in the text, which basically is a table that consists of the symbol, a short explanation and the dimension it has as indicated below: ...