Recent content by LightPhoton

In A Modern Approach to Quantum Mechanics, Townsend writes: One of the most evident features of the position-space representations (9.117), (9.127), and (9.128) of the angular momentum operators is that they depend only on the angles ##\theta## and ##\phi##, not at all on the magnitude ##r##...

Answers to questions like this assume that the quantum state in a Hilbert space is only a function of time, that is ##\partial_i\vert\psi(t)\rangle\neq0## only when the variable ##i## is ##t##. Is this a postulate of standard quantum mechanics, that in Schrödinger's equation the state in...

Wikipedia says that the equation in the title is defined to be true. But is it true always? Working with the right-hand side, $$\langle \mathbf r\vert\hat A\vert\Psi\rangle=\int\langle \mathbf r\vert\hat A\vert\mathbf r'\rangle\langle\mathbf r'\vert\Psi\rangle\ d\mathbf r'$$ If we assume...

The Gibbs sum is given by $$Z=\sum[\lambda \exp(-\varepsilon/\tau)]^N$$ where ##\lambda\equiv\exp(\mu/\tau)##. Since we are assuming ##\mu>\varepsilon##, we take only the last term of the sum because all others can be neglected. thus $$Z\approx[\lambda \exp(-\varepsilon/\tau)]^N$$ Now...

I am following this video and; Eisberg and Resnick's Book for this derivation, for I cannot find other sources that go as in-depth as they do. $$\Large\text{Question 1)} $$ Jean's cube, or the metallic cube, is assumed to be a perfect absorber. On this fact alone, authors state Now assume...

Kittel and Kroemer derive the pressure of a statistical state in the following way: They assume a volume compression of a system such that the quantum state of the system is maintained at all times; thus, the entropy ##(\sigma)## is constant in the process of compression. Now let the energy of...

##\vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} \Rightarrow \vec a\cdot(\vec{b} - \vec{c})=0 ## From where What Kuruman says applies

In Classical Electromagnetic Radiation, Heald and Marion take the divergence of Faraday's and Ampere-Maxwell's laws and state: $$-\vec\nabla\cdot\frac{\partial\vec B}{\partial t}=\vec\nabla\cdot\vec\nabla\times\vec E=0$$ If we assume that all the derivatives of B are continuous, we may...

TL;DR Summary: Looking for cosmology books with manuals Any such book available? The only one that I could find is by James Rich. It's an okayish book but any other alternatives? Ryden is also one but it's not advanced/rigorous enough for me.

In A short course in general relativity, Foster and Nightingale write: So in modern astronomy, how is this apparent paradox resolved?

Now that I have had a chance to read it carefully, I understand your point along with Orodruin's. However, how do we reconcile this with the idea that ##g_{\mu\nu} = \vec e_{\mu} \cdot \vec e_{\nu}##? As you showed, only the time-time component of ##g_{\mu\nu}## survives, which implies that...

We want to relate acceleration in two frames, an inertial frame S, and the instantaneous inertial reference frame of the particle on which it is being accelerated, S', which is moving in the ##x## direction at the moment. Let the acceleration in S be ##(a_x,a_y)## and in S' be ##(a_x',a_y')##...

How is the angle between two 4-vectors defined in special relativity? Consider two 4-velocity vectors: $$U^\mu=(1,0), \\ V^\mu=\gamma_{rel}(1,v_{rel})$$ Where the vectors are written in the frame of the particle with ##U^\mu##. The dot product between these is $$U^\mu V_\mu=\gamma_{rel}$$ If...

Thanks for the quick reply! It is well above me for now (and a similar answer I got on StackExchange is as well, https://physics.stackexchange.com/questions/842622/spacetime-interval-in-galilean-relativity#842629) so I am not able to fully appreciate the content you shared. Can you kindly...

In this [1] video, EigenChris mentions that there is no spacetime distance in Galilean relativity. And in this [2] video he replies to a comment as follows: > @hariszachariades8299: If the "spacetime separation vector" has components ##(\Delta x,\Delta t)##, there is no combination ##a\Delta...