24 votes

Does the earth’s rotational angular velocity change?

The Earth is not a single rigid body, but consists of at least five separate regions which can move relative to one another. These are the crust (which is the region that we use to measure day length),...
  • 36.7k
13 votes
Accepted

Where is the reaction force of an object that has just flung out from a circular motion?

While an object is in uniform circular motion, the force that is acting upon it is directed to the center. This force is what prevents the object moving linearly if the force suddenly vanished. If ...
  • 25.8k
12 votes

Does the earth’s rotational angular velocity change?

To add to @gandalf61's answer: You can also look up solar time. Due to the orbit around the Sun, the Earth has to rotate a bit more than 360° for the sun to get back to the same apparent position in ...
10 votes

How to derive the the asymptotic momentum of a classical electron after it is ionized by a strong laser field

Introduction The short answer is that the expression in the paper contains a misprint, and that it is indeed possible to prove it and to provide a construction that shows why it should have this form. ...
7 votes

Where is the reaction force of an object that has just flung out from a circular motion?

This is part of why centrifugal forces are often called "fictitious." Newton's laws of motion only apply in an inertial reference frame. The moment you move into accelerating reference ...
  • 20.8k
5 votes

Doubt tensor product states of bipartite system

The ability to relocate numbers $(\lambda {\bf a})\otimes {\bf b}={\bf a}\otimes (\lambda {\bf b})= \lambda({\bf a}\otimes {\bf b})$ is part of the definition of the tensor product.
  • 43.3k
5 votes

Does the earth’s rotational angular velocity change?

There is no “gravitational” source of external torque acting on the earth Yes, there is. The tides are caused by the Moon's gravity. That energy has to come from somewhere. The drag caused by the ...
3 votes
Accepted

Eigenvalue problem of $L_z$

From Shankar's QM book pg. 313... $$-i\hbar \frac{\partial \psi(\rho,\phi)}{\partial \phi}=l_z\psi(\rho,\phi)$$ The solution to this equation is $$\psi=R(\rho)e^{i l_z\phi/\hbar}$$ I'm going to drop ...
  • 9,427
2 votes

Questions on Peter Woit's Proof of the Clebsch-Gordan Decomposition Theorem

In the decomposition $$ V_{j_1}\otimes V_{j_2} = \oplus_i V_{J_i}$$ you have on the one hand the natural basis $\lvert j_1m_1j_2m_2\rangle = \lvert j_1m_1\rangle \otimes \lvert j_2m_2\rangle$ of the ...
  • 111k
2 votes

Why rotation is not an observable?

An operator $A$ acting over a state $|\psi\rangle$ is an observable if $A=A^{\dagger}$ (it is its own self-adjoint or transpose conjugate). What this means is that the eigenvalues of the operator are ...
  • 3,318
2 votes

Eigenvalue problem of $L_z$

First of all, I would like to point out that $l_z$ must be real for a very fundamental reason: eigenvalues of Hermitian operators must be real. Let me prove this very quickly. I'll not use the Dirac ...
  • 30.9k
2 votes

Wavefunction with two different values at same point

$l$ must be an integer, otherwise $P_{l}(x)$ is unnormalizable. So is $m$ since $m=-l,\cdots,l-1,l$. Mathematically, the logic is that $m$ should be an integer, otherwise eigenfunctions of $L_z$ are ...
  • 399
1 vote

Physical difference between $\vert S=0, m = 0 \rangle$ and $\vert S=1, m = 0 \rangle$?

In context of a two spin $\frac{1}{2}$ particle systems, we know that, $\vert S=0, m = 0 \rangle = \frac{1}{\sqrt2}(\vert\uparrow\downarrow\rangle - \vert\downarrow\uparrow\rangle)$ $\vert S=1, m = ...
  • 9,427
1 vote
Accepted

Relativistic invariants of a classical field in 4D fashion: why the relation between the components of the current density holds?

The definition of $dS^i$ (Landau §6) is that it is a four-vector equal in magnitude and normal to the hypersurface element; in other words, $dS^i$ is the projection of the hypersurface element, ...
1 vote

Need help with solution on a physics calculation involving newtonian mechanics - (angular momentum)

To solve properly a problem in mechanics, it is strongly advised to follow these steps: Clearly identify the system and the frame of reference: System: Wheel+pulley_mass. Reference frame: the road. ...
  • 1,625
1 vote

Eigenvalue problem of $L_z$

I'll write what other people have written but in a slightly different way. Let's start at the beginning with the eigenvalue problem $L_z\psi=\ell_z\psi$. As you stated, in polar coordinates, this is ...
  • 36
1 vote

Eigenvalue problem of $L_z$

I haven't read Shankar, but it seems to me that if you are looking for functions $\psi(\rho, \phi) = R(\rho) e^{i l_z \phi / \hbar}$ that are continuous and smooth at every point in space, it must be $...
  • 1,838
1 vote
Accepted

How to prove $\exp(-\frac{i}{2} \theta (e.J)) = I \cos(\frac{\theta}{2})- i( e.J) \sin(\frac{\theta}{2}) $

I'll continue with $\boldsymbol \sigma=(\sigma_1,\sigma_2,\sigma_3)$ instead of $\boldsymbol J$ to represent the Pauli matrices. To prove Eq(1): The commutators and anti-commutators between Pauli ...
  • 399
1 vote

Conservation of angular momentum across different reference frames?

For the case where the axis of rotation is taken to be at the point of contact of the ball on the table, and if the ball slips, the axis is not stationary in an inertial frame since the point of ...
  • 7,016

Only top scored, non community-wiki answers of a minimum length are eligible