Recent content by WeiShan Ng

Homework Statement I am revising on the derivation of the differential equation of energy (White's Fluid Mechanics 7th ed) and I'm having trouble understanding the sign convention used in the viscous work term. The textbook first define an elemental control volume and list out the inlet...

I found the derivation in "Gravitation and Cosmology" by Weinberg at pp.421-424

The definition of the angular diameter distance is the ratio of an object's physical transverse size to its angular size. However when I was reading my textbook, *Astrophysics in a Nutshell by Dan Maoz pp.220-221*, I am having some trouble trying to understand the notion of **angular diameter...

Thank you!

Homework Statement Hi, I was reading Griffiths and stumble upon some questions. This is from 5.1.2 Exchange Forces. The section is trying to work out the square of the separation distance between two particles, $$\langle (x_1 - x_2)^2 \rangle = \langle x_1^2 \rangle + \langle x_2^2 \rangle -...

I'm still trying to get my head around this, not sure if I understood it correctly... When we write ##|\Psi\rangle##, it means we haven't specify any particular basis set to represent the state vector, when we write ##\Psi(x)##, it means we are writing the component of ##|\Psi\rangle## along an...

These are from Griffith's: My lecture note says that I am having quite a confusion over here...Does the ##\Psi## in the expression ##\langle f_p|\Psi \rangle## equals to ##\Psi(x,t)##? I understand it as ##\Psi(x,t)## being the component of the position basis to form ##\Psi##, so...

I am confused about the difference between the two In Griffith's 2.3 The Harmonic Oscillator, he superimposes the quantum distribution and classical distribution and says What I understand for quantum case is that ##|\Psi_{100} (x)|^2## gives the probability we will measure the particle...

Thanks for your help! I will try to redo the question in Cartesian coordinates.

I try to walk through the steps to see where I have done wrong: Writing the cross products in Cartesian coordinates I have $$[\mathbf{\hat{r}\times (\hat{r}\times \hat{z})}] = \frac{xz}{r^2} \mathbf{\hat{x}} + \frac{yz}{r^2} \mathbf{\hat{y}}+\frac{x^2-y^2}{r^2} \mathbf{\hat{z}}$$ where ##r^2 =...

Alright I found my own errors, turns out ##[\mathbf{\hat{r}\times \hat{r}\times \hat{z}}] = -\sin \theta \cos \theta \cos \phi \mathbf{\hat{x}}+ \sin \theta \cos \theta \sin \phi \mathbf{\hat{y}} + - \sin^2 \theta \mathbf{\hat{z}}## and since ##\theta = \pi/2## in xy plane, I can write $$\Phi =...

Homework Statement A point charge q sits at the origin. A magnetic field ##\mathbf{B} (\mathbf{r})=B(x,y)\mathbf{\hat{z}}## fills all of space. The problem asks us to write down an expression for the total electromagnetic field angular momentum ##\bf{L_{EM}}##, in terms of q and the magnetic...

I don't think ##y## and ##\ddot y## will be in the same direction, as this is a damped oscillator. The direction of ##\vec{T}## will be depending on the magnitude and direction of the ##y(t)##, if ##y(t)## is acting downwards, then ##\vec{T}## will always be acting downwards. If ##y(t)## is...

I don't think ##y## and ##\dot y## would be necessarily in the same direction, as we can have negative velocity at the instant we are at positive coordinate. This applies to ##\dot y## and ##\ddot y## too.

Oh I think I know where I get it wrong! So if I define the resistive force ##\vec{R}##, the tension from the spring ##\vec{T}##, and the weight ##\vec{W}##: $$\vec{R} = -\beta \dot{y} \hat{y} \\ \vec{T} = -ks \hat{y} - ky(t) \hat{y} \\ \vec{W} = mg \hat{y}$$ Then I use vector addition to...