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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8
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118 views

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

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 ...
4
votes
3answers
306 views

Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
0
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0answers
10 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 &...
3
votes
2answers
176 views

Problem with derivation of phonons in crystal

In this derivation of phonon solutions, everywhere, we are forcefully assuming the wavelike characteristics along the length of the chain. While all we can deduce for finding out the fundamental ...
2
votes
1answer
90 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 ...
0
votes
2answers
47 views

How do we determine the location of particles?

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
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0answers
60 views

What does the Free Will Theorem Imply?

Sorry if discussion of the Free Will Theorem belongs in the philosophy section, but as it is in the realm of physics too, I thought I would post it here instead... If we have a free will in the ...
0
votes
1answer
53 views

Applying angular momentum operator

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
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0answers
26 views
3
votes
1answer
37 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 ...
6
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8answers
2k views

Prove that an electron in a hydrogen atom doesn't emit radiation [duplicate]

According to electrodynamics, accelerating charged particles emit electromagnetic radiation. I'm asking myself if the electron in an hydrogen atom emits such radiation. In How can one describe ...
0
votes
0answers
4 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 ...
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0answers
28 views

Average magnetic dipole moment [on hold]

An electron in the hydrogen atom is described by the wavefunction: $$ \Psi = 0.5773\left(\psi_{431} + \psi_{432} + \psi_{321} \right) $$ where the $\psi_{nlm}$ are the eigenfunctions of the ...
0
votes
1answer
48 views

How to make an intuitive sense of the definition of Hermitian adjoint? [on hold]

How to make an intuitive sense of the definition of Hermitian adjoint? Why it is defined in that way? What is the different between operators and matrices?
11
votes
4answers
567 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
votes
0answers
22 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_\...
1
vote
1answer
239 views

Thought Experiment: Force on magnets in a Stern Gerlach Experiment

Background: In the SG experiment, an inhomogenous magnetic field affects a force on particles passing between two magnets. "Measurement" takes place when a screen is placed on one end, blocking one ...
0
votes
1answer
25 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 ...
1
vote
2answers
32 views

Understanding Zeeman Splitting

I'm reading a standard modern physics history book ("Inward Bound" by A. Pais), and I realized I don't really understand Zeeman splitting well. In the section I'm reading, there's a short discussion ...
-1
votes
0answers
29 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=\...
54
votes
3answers
7k views

Is it possible to “see” atoms?

As per my knowledge, atoms are small beyond our imaginations. But there is an image on Wikipedia that shows silicon atoms observed at the surface of silicon carbide crystals. The image: How can we ...
-1
votes
1answer
492 views

Dirac Delta Potential and bound/scattered states

Why does the attractive Dirac Delta distribution (function) potential $V = \alpha\delta$(x) (for negative $\alpha$) yield both bound AND scattered states? Is this due to the definition of the Dirac ...
-2
votes
0answers
30 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?
0
votes
2answers
87 views

Can two different objects or system of molecules have different temperatures, but having same internal kinetic energy?

If I take an extreme case, where a body has only an internal potential energy with zero internal kinetic energy, does this body have a temperature? Another question related to it: if two objects A and ...
0
votes
3answers
103 views

Significance of wave number?

Till now all I know about the wave number is its formula i.e. ${\frac{2\pi}{\lambda}}$. I always wanted to know what it really means. So can anyone please, explain me its physical significance?
0
votes
1answer
40 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 ...
3
votes
1answer
25 views

What happens to the energy of fermions when a degenerate gas forms?

For example, when an electron degenerate gas forms, two electrons (of opposite spins) occupy each of the lowest possible energy states up to the Fermi energy. This is because of the Pauli exclusion ...
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votes
0answers
49 views

Expectation value of an Observable and Eigenstates

I am learning about Quantum Mechanics at the moment and I was wondering about Eigenfunctions and Observables. The question I would like to ask is, If a wavefunction is not an eigenstate of an ...
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votes
0answers
39 views

This might make no sense light is time [on hold]

I've done a lot of research on time I think when light/color is absorbed it is giving off as time and when it is going fast the light can't keep up
1
vote
2answers
163 views

Quantum probability of entangled spin-1/2 particles?

Let us say that you have two entangled spin-1/2 particles (entangled in such a away that angular momentum is conserved). Let us say particle 1 moves to the left and particle 2 to the right. We measure ...
0
votes
1answer
118 views

Reduced density matrix

During a course on quantum mechanics we've been talking about density matrices. Now I came across the following exercise. Consider a two spin $\frac{1}{2}$ systems, labeled 1 and 2. Calculate: ...
3
votes
3answers
176 views

Is my understanding of the delayed choice quantum eraser correct?

I'll say in advance that I am by no means an expert on Quantum Mechanics. I understand the basic mathematics of it (Wave function and Schrodinger equation), but did not go deeply into it or study it ...
5
votes
1answer
68 views

One particle states in an interacting theory

Question: What is the general definition of one particle states $|\vec p\rangle$ in an interacting QFT? By general I mean non-perturbative and non-asymptotic. Context. 1) For example, in Weigand'...
3
votes
2answers
91 views

The meaning of 'coupling'?

In quantum mechanics if two quantities $A$ and $B$ are said to be coupled what does this actually mean? I would guess that it means we have a term like $A\cdot B$ in the Hamiltonian but this is only ...
3
votes
1answer
136 views

A question on the Chern number and the winding number?

Let $\mid \psi(x,y) \rangle$ be a normalized wavefunction living in a $d$-dimensional Hilbert space and depend on two real parameters $(x,y)$ that belong to a closed surface (e.g., $S^2, T^2$, ...). ...
2
votes
0answers
49 views

$\left< \frac{\partial (xp)}{\partial t} \right> = 0$ When is this true?

Is this always true in quantum mechanics? $$\left< \frac{\partial (xp)}{\partial t} \right> = 0$$ I encountered this when working problem 3.31 in Griffiths Introduction to Quantum Mechanics II....
0
votes
0answers
16 views

Why must the separation constant be real in a time dependent wave function?

I'm not sure if I'm asking this right. I'm reading ''Introduction to Quantum Mechanics'' by Griffiths and in the chapter 2 exercises he asks to prove that the separation constant, $E$, must be real. ...
4
votes
2answers
365 views

Off-diagonal elements of Hamiltonian matrix $H_{12}$ & $H_{21}$: energy of transition from $|1\rangle$ to $|2\rangle$ or amplitude of transition?

$$ \newcommand{\k}[1]{\left| #1 \right\rangle} \newcommand{\dd}[1]{\frac{d #1}{dt}} $$ In a Hamiltonian Matrix like this: $$H = \begin{pmatrix} E_{11} & E_{12} \\ E_{21} & E_{22} \end{...
0
votes
3answers
183 views

Treating matter waves as light waves?

Is it valid to treat a matter wave as a light wave with wavelength equal to the de Broglie wavelength of the matter wave? Either way please can you explain why?
1
vote
1answer
68 views

Is the MWI symmetric in time?

Reading the blog of Sean Carroll (I recognize he isn't the only voice) has made me more sympathetic to the notion of many worlds, but reading Susskind (also not the only voice) has made me think that ...
-6
votes
0answers
32 views

quantum mechanics problem orthonormal function [on hold]

$$\psi_n(x)=\sqrt{\frac{2}{a}}\sin\left(\frac{\pi n}{a}x\right)$$ is this wave function orthonormal or not? If yes then prove it.
0
votes
1answer
66 views

Practical way of expressing the $\delta$-function [on hold]

I have got a problem in using the $\delta$-function. As we know, this function is often used to define a 'density'-related quantity. Such as the density of states or some correlation function. Take ...
14
votes
1answer
283 views

Do Franck-Condon oscillations have natural lineshapes?

I recently found a paper (for the curious, this one) that talks about observing the motion of a nuclear wavepacket in H2O, as initiated by tunnel ionization. This wavepacket should be thought of as a ...
2
votes
3answers
57 views

Two qubits system in polar co-ordinates

I know that I can write a single qubit state in terms of polar co-ordinates $(r,\theta,\phi)$ on a Bloch sphere. \begin{equation} \rho = \begin{pmatrix} \frac{1+r \cos\theta}{2} &\frac{r \exp(-i\...
3
votes
1answer
147 views

Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
4
votes
2answers
759 views

What causes Potassium to decay into Argon the way it does

From evolutionwiki: "Potassium 40 decays into argon 40 through a process known as electron capture. In electron capture, an electron from the innermost electron shell "falls" into the nucleus, ...
11
votes
1answer
234 views

Significance of the exception to Gleason's Theorem when n = 2

Gleason's Theorem famously asserts that (appropriately defined) measures on the lattice of a complex Hilbert space can be implemented by density operators via the trace operation, except in the case ...
-4
votes
2answers
48 views

How to resolve “bottleneck” of encoding input of quantum computer? [on hold]

As far as I understand, all quantum computing purpose is to accelerate exponentially (upon input length) computation time of given task. But here user faces bottleneck to serialize input, and ...
13
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1answer
390 views
+50

Does measurement, quantum in particular, always increase the total entropy?

Measurement of a quantum observable (in an appropriate, old-fashioned sense) necessarily involves coupling to a system with a macroscopically large number of degrees of freedom. Entanglement with this ...