# Tagged Questions

1answer
83 views

### Crystal Momentum in a Periodic Potential

I'm working through some basic theory on periodic potentials, and I would appreciate help in understanding the crystal momentum. Suppose we have a Bravais lattice with lattice vectors $\textbf{R}$. ...
1answer
358 views

### Energy conservation limited by uncertainty principle

The way I learned it from practicing Fourier analysis and signal processing besides quantum mechanics, is that Energy conservation cannot be achieved in short time scales, and that limits energy ...
1answer
52 views

### Regarding derivation of Probability Current

The question for the full derivation of Probability Conservation -> Probability Current was already asked here: Probability current. I apologize for not retyping it out, but it's already beautifully ...
0answers
95 views

### Orbital angular momentum selection rules for three identical particles

I'm trying to figure out if there are selection rules for the total orbital angular momentum for a system of three identical particles, say bosons. For two identical bosons one can argue that the ...
1answer
68 views

### What is the difference between the process in which energy converts to matter and that in which it converts to antimatter?

What is the difference between the process in which energy converts to matter and the process in which it converts to antimatter? In colliders, for instance, is the product (either being the matter or ...
1answer
99 views

### Quantum explanation of Newton's Third Law of Motion

Newton's law states that for every action there is equal and opposite reaction. This law explains how rockets fly in space and accounts for the the majority of the lift action generated by a ...
3answers
142 views

### Rotational invariance and operator-squares

My mind is drawing a blank right now. In systems with spin and orbital angular momentum, I know that rotational invariance implies that $[H, \mathbf{J}]=0$ where $\mathbf J=\mathbf L+\mathbf S$. But ...
2answers
129 views

### Proof of conservation of information [duplicate]

After listening of some lectures of Leonard Susskind about black holes, he mentioned that conservation of information is one of the foundations of physics. After searching the web I cannot seem to ...
4answers
337 views

### Detecting a photon without changing it: Does it break conservation laws?

This is about an article published on ScienceMag: Nondestructive Detection of an Optical Photon. I don't have access to full text, but you can see a brief transcription in this link. Basically, it ...
0answers
141 views

### Is total angular momentum conserved in particle interaction?

Imagine that two electrons interact by exchanging a virtual photon. I know that the total energy and linear momentum of the two electrons is conserved by the interaction. Is the total (orbital) ...
1answer
181 views

### Question on conserved quantities and Noether's theorem

I have a question about Noether's theorem in the context of QM, which I'll state in the context of the weak interaction but the basic point could be generalized. According to Noether's theorem, given ...
0answers
90 views

### Collision of 2 neutrons

If two neutrons collide in 3D space and we want to determine the final velocities of both nuetrons (3 components for each neutrons), we can use the conservation of momentum equations and the ...
1answer
303 views

### Can 3 photons be combined to give a spin-0 projection?

Motivation: The neutral pion decays to 2 photons ($\pi^0\to\gamma\gamma$) most of the time. For the decay of the neutral to 3 photons ($\pi^0\to 3\gamma$) we have an upper limit on the branching ...
2answers
821 views

### Quantum Mechanics: Show that the expectation value of angular momentum does not change with time

The potential is given by $V\left(\left\|(x,y,z)\right\|\right)$, so $[\hat{L}, \hat{H}] = 0$. Using the definition of $\langle \hat{L} \rangle$ and the time-dependent Schrödinger equation, show that ...
3answers
2k views

### Noether theorem, gauge symmetry and conservation of charge

I'm trying to understand Noether's theorem, and it's application to gauge symmetry. Below what I've done so far. First, the global gauge symmetry. I'm starting with the Lagragian ...
1answer
330 views

### What conservation law corresponds to this local $U(1)$ symmetry of the CCR?

It is known that canonical commutation relations do not fix the form of momentum operator. That means that if canonical commutation relations (CCR) are given by ...
1answer
913 views

### A Short way to show Conservation of Quantum Laplace–Runge–Lenz Vector?

I had been asked to prove the conservation of Quantum Laplace–Runge–Lenz Vector: ...
1answer
502 views

### How did one get the defining equation of probability current and conservation of probability current and density?

I'm reading the Wikipedia page for the Dirac equation: $$\rho=\phi^*\phi$$ and this density is convected according to the probability current vector J = ...
1answer
203 views

### Entanglement and conservation

Is the following assertion sufficiently unique to merit a paper? Every absolute conservation law implies a corresponding form of entanglement, not just spin (angular momentum). Linear momentum ...
1answer
1k views

### Probability current

Conservation of probability: Suppose a wavefunction has ${\partial \mathbb P \over \partial t} = -t f(x,t)$ and ${\partial j \over \partial x} = i f(x,t)$. How does it follow that \${\partial \mathbb P ...
5answers
2k views

### What is the conserved quantity of a scale-invariant universe?

Consider that we have a system described by a wavefunction psi(x). We then make an exact copy of the system, and anything associated with it, (including the inner cogs and gears of the elementary ...