Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the quantum-field-...

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17 views

Darwin term affecting hydrogen s-states

The Darwin term, a correction to the non-relativistic hydrogen Hamiltonian due to the zitterbewegung of the electron, is given by $$H_{Darwin}=\frac{e^2\hbar^2}{8m^2c^2\epsilon_{0}}\delta^3(\...
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3answers
54 views

Measuring different components of spin simultaneously

I'm reading Griffiths Introduction to QM and I'm having trouble understanding why you can't simultaneously measure the x,y and z components of spin. I know that the uncertainty principle prevents this ...
9
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0answers
36 views

Are there exact analytical solutions to the electronic states of the hydrogen molecular ion $\mathrm H_2^+$?

The hydrogen molecular ion (a.k.a. dihydrogen cation) $\mathrm H_2^+$ is the simplest possible molecular system, and as such you'd hope to be able to make some leeway in solving it, but it turns out ...
5
votes
1answer
132 views

How did Heisenberg come up with matrix mechanics?

I have learnt that matrix mechanics came before Schroedinger's wave mechanics, however introductory quantum mechanics textbooks introduce you to wave mechanics first. The way in which the transition ...
0
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1answer
130 views

Classical Mechanics as an approximation of Quantum mechanics [closed]

I want to show an equality: We know from Ehrenfest's theorem that $$ \frac{d \langle x \rangle(t)}{dt}= \left\langle \frac{\partial H}{\partial p} \right\rangle $$ I'd like to derive the ...
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2answers
294 views

Atomic Weight and Time Dilation

So, this might sound kind of ridiculous but I was thinking about Relativity and since Gravity is a warping of Space-Time, or Time Dilation, why don't we measure Atomic Mass in Units of Time Dilation? ...
5
votes
2answers
105 views

Why doesn't this experiment violate the Uncertainity Principle?

Is it possible to slow an electron in such a way(for example using a cyclotron to decelerate the electron ) that it completely stops. And since we created the slowing mechanism we might be able to ...
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1answer
100 views

How is hydrogen fine structure currently accounted for? [closed]

At a usually reliable site, Hyperphysics, the fine structure of Hydrogen is accounted for by the interaction between the B-field generated by the orbit of the electron, $0.4\:\mathrm{T}$ at $1s$ and $...
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0answers
40 views

Can a quark be changed to a different flavour?

For example, is it possible to change an up quark into a down quark or vice versa? If so, what is the practical process for doing such a thing? What is the theory behind it? For an example, lets say ...
3
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0answers
44 views

Energy term in Wavefunction Normalization

I recently started learning quantum mechanics and when I solved the Schrödinger equation for the Hydrogen atom, in particular the Radial equation, I found that I had normalized it but a term in the ...
0
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0answers
32 views

Must entangled particles be connected by some means to stay entangles

The people on this site are far more knowledgeable than I am and I probably don't belong here but my questions always seem to get answered to my satisfaction and I end up learning something. I have ...
0
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1answer
42 views

counting normal modes

I'm not sure if my confusion is substantive or merely semantic. So here's the most naïve way to frame it: A free $N$-atom molecule has $3N-6$ vibrational normal modes, with each mode having fixed ...
4
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1answer
52 views

When and why are effective Hamiltonians used?

I'm wondering, are there general physical principles behind writing down quantum evolutions in terms of effective Hamiltonians? I'd love a kind of big-picture explaination of their use. For example, ...
-4
votes
1answer
78 views

Where do people go (online) to present big ideas they have discovered? [closed]

I can't realistically travel, but is there somewhere online where I can present some ideas? Or do I just put it on arXiv and hope someone important reads it?
5
votes
1answer
167 views

When particle number can change in quantum physics?

Let me write a paragraph from D.Tong lecture notes on QFT-chapter2 when he is talking about non-relativistic limit of scalar quantum field theory : A related fact is that the conserved charge $Q=\...
2
votes
0answers
46 views

How does the Pauli-exclusion principle work if space is infinitely divisible?

How does the Pauli-exclusion principle work if space is infinitely divisible? Naively any two fermions should always be in different quantum states unless they are separated by an infinitesimally ...
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0answers
11 views

Energy independent tunneling rate

I was wondering if there are any examples of potential barriers for which the tunneling probability is independent of particle energy (ignoring any infinities of course). It seems that from the WKB ...
-1
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1answer
50 views

Infinite square well - periodic boundaries

If we have an infinite square well, I can follow the usual solution in Griffiths but I now want to impose periodic boundary conditions. I have $\psi(x) = A\sin(kx) + B\cos(kx)$ with boundary ...
2
votes
1answer
37 views

Is the variational method valid when discrete spectrum eigenfunctions are in finite number?

In the proof of the variational method to estimate the ground state energy of a system, that is $$ \newcommand{\ket}[1]{\lvert{#1}\rangle} \newcommand{\bra}[1]{\langle{#1}\rvert} \newcommand{\braket}[...
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0answers
20 views

Eigen energy of the Landau levels in a tilted magnetic field

The problem pertains to a fermi gas in a tilted magnetic field confined by a harmonic potential in the z direction. I chose the vector potential $(0,ax-bz,0)$. I obtain the following hamiltonain with ...
0
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0answers
31 views

Invariance of State Vector under Two Operations

I am trying to understand why if you measure one non degenerate operator you get a new state w1v let's say with w1 eigenvalue, then let's say u measure a new operator that has degenerate eigenvalue v ...
3
votes
1answer
58 views

Is there an angular velocity operator in quantum mechanics?

In classical mechanics we can write as velocity of a rotating object $\vec{v} = \vec{\omega} \times \vec{r} $ or in analogy the momentum $\vec{p} = m (\vec{\omega} \times \vec{r})$ using the angular ...
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2answers
44 views

How does the uncertainty product $\Delta x \Delta p$ behave for the bound states of the triangular potential?

As has been remarked earlier, if you take an unbounded potential $V(x)$ (so that all the eigenstates are bound) and you look at the uncertainty product $\Delta x\Delta p$ as a function of the index $n$...
1
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2answers
82 views

De Broglie- Bohm Quantum Theory

From what I have read the Standard Model of Particle Physics uses quantum mechanics,special relativity, along with other assorted mathematics to make predictions and provide a framework for QED, QCD, ...
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0answers
76 views

Why don't we have to go through the Lagrangian in QM? [duplicate]

In classical mechanics, I remember whenever we calculated the Hamiltonian, we'd first have to calculate the Lagrangian, and then we'd get the Hamiltonian through the definition: $$H= \sum\dot q_ip_i-...
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1answer
42 views

Quantum vacuum thruster and conservation of momentum [duplicate]

I have been reading about the quantum vacuum thruster on Wikipedia and I think I understand the idea of virtual particles being created and destroyed but what I don't understand is how this is ...
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0answers
30 views

How to apply the time evolution operator on a 2 level system

I'm struggling to understand how to actually solve analytically the time evolution of a given initial state with the Hamiltonian \begin{equation} H =\epsilon*\sigma_z + \Delta*\sigma_x, \end{equation} ...
1
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1answer
37 views

Why can precomputed sets of lattice QFT field configurations be used to measure arbitrary observables?

My knowledge of quantum mechanics is rusty and my understanding of (lattice) quantum field theory on a very novice level at best, so it is likely my whole question is based on completely wrong ...
-5
votes
0answers
23 views

about the motion of electrons inside the atom [duplicate]

My question is very basic question.I am somehow not able to understand it. bohr's theory says that the electron can only revolve in orbits which they have quantised angular momentum so they must ...
12
votes
2answers
987 views

How should Dirac notation be understood?

If vectors $|\vec{r}⟩$ and $|\vec{p}⟩$ are defined as $$ \hat{\vec{r}} |\vec{r}⟩ = \vec{r} |\vec{r}⟩ \\ \hat{\vec{p}} |\vec{p}⟩ = \vec{p} |\vec{p}⟩ $$ then one can see that products like $$ ⟨\vec{...
-4
votes
0answers
20 views

Function of operator quantum mechanics [duplicate]

Help me to prove this $$e^Ae^B=e^{A+B}e^{\frac{1}{2}[A,B]}$$ $A$ not commute with $B$, but $A and $B commute with $[A,B]$.
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0answers
11 views

Specific microstate(s) corresponding to total angular momentum quantum number

Given a certain number of electrons in a certain electronic configuration (say, d$^2$ or (n$_1$p)(n$_2$d)), all combinations of the quantum numbers $m_l$ and $m_s$ can be constructed. Each of these ...
4
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1answer
89 views

Understanding the relationship between Phase Space Distributions (Wigner vs Glauber-Sudarshan P vs Husimi Q)

I am moving into a new field and after thorough literature research need help appreciating what is out there. In the continuos variable formulation of optical state space. (Quantum mechanical/Optical)...
3
votes
1answer
61 views

Quantum master equation and off diagonal terms

I have a couple of related questions What is exactly the difference between the quantum master equation and the regular master equation? My understanding is that the normal master equation is used ...
0
votes
1answer
34 views

Group Velocity of guassian packet equals time derivative of mean position?

If I look at a gaussian wave package, and then interpret (in the usual Quantum-Mechanics Way) its square value as the propability density, then I can calculate a mean value for the position: $$ x_{...
5
votes
1answer
143 views

What is the difference between active and passive transformations in Quantum Mechanics?

I am trying to understand what each transformation means and what their differences are but many books that don't state which transformation they are referring to make it a bit confusing to understand ...
10
votes
1answer
369 views

In quantum mechanics, how exactly do we associate Hermitian operators to classical observables? [duplicate]

In a first course on quantum mechanics, everybody learns some version of the following statement: Postulate: To every classical observable $A$ of a physical system, there corresponds a Hermitian ...
0
votes
1answer
26 views

Selection rules for electric quadrupole radiation

The selection rules for electric quadrupole radiation in a Hydrogen-like atom are: $$ \begin{aligned} \Delta l &= 0,\pm2 \hspace{1cm}(l=0\leftrightarrow l'=0 \textrm{ is forbidden}) \\ \Delta m &...
0
votes
2answers
76 views

How do we determine the location of particles? [closed]

Can someone explain how the location of a particle is determined both theoretically and experimentally (if possible)? Can the location of a particle be given by the uncertainty principle? (dividing ...
3
votes
1answer
61 views

Can Light Waves Be Irregular?

From what I understand, electromagnetic radiation produced by an antenna is of the frequency that corresponds to the motion of the electrons moving around in the antenna. And I assume that the ...
0
votes
1answer
75 views

Applying angular momentum operator [closed]

How are the algebraic steps to applied the angular momentum operator defined as: $$\hat{L}=-i\hbar[r\times\nabla]$$ to $$\Psi=a~ \psi_{431}$$ where the $\psi_{nlm}$ are the eigenfunctions of the time ...
3
votes
0answers
42 views

Calculating 2 particle Partial Trace for Density Matrix in Zeeman basis for a large number of Spins

I want to trace out all spins but 2 from a density matrix in the zeeman basis for N spins. For N=3 for example I would have the basisvectors: $ |S=1.5, m=-1.5\rangle =|000\rangle, |S=1.5, m=1.5\rangle ...
0
votes
0answers
37 views

Relative velocity between phase velocity wave and a group velocity wave

It is said that material particles have a dual nature. A particle is associated with a wave which travels with phase velocity and the particle travels with group velocity. These are related by $$v_\...
-3
votes
0answers
36 views
0
votes
1answer
52 views

Number of electrons in conduction band

As mentioned in a previous question, the number of electrons in conduction band in a semiconductor can be computed as follows: $$N = \int_{E_c}^{+\infty} g_c(E)f(E)dE$$ where $g_c(E)$ is the density ...
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votes
0answers
30 views

Is my understanding of creation/annihilation operators' functional dependency correct?

I am trying to gain a little intuition about second quantisation, specifically about creation/annihilation operators. Lets say you quantise the free EM field (in 1d) and end up with the usual: $H=\...
3
votes
1answer
111 views

How to evaluate possible values of spin of two photon system?

Photon hasn't well defined quantity such as spin. Instead of it, it is characterized by helicity $h$. Let's assume state of two photons in CM frame (with $\mathbf k$ being the momentum of one of ...
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votes
0answers
32 views

what is the rough motion of an electron in an atom [duplicate]

If The Uncertainity principle is true,then how does an electron move ?if the motion cannot be random also,then how does it occur?
15
votes
4answers
719 views

Curvature of Hilbert space

That may appear as a dumb question, but: Does Hilbert space have curvature, or is it a flat space? How and why?
0
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1answer
48 views

Uncertainty and Classical waves

My professor, introducing Heisenberg uncertainty principle, started from the Fourier transform and the classical uncertainty for waves. He told about the localized impulsive wave $\delta(x)$ which ...