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 ...

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2answers
602 views

What happens to the wavelength/frequency of a photon as it passes through an event horizon?

I've asked a similar question about photons and black holes but wanted to rephrase it more specifically, so here goes... Ever since I learned how a photon's wavelength and frequency are indivisibly ...
3
votes
1answer
630 views

Spin-orbit coupling constant for rubidium

I have come across the following question in my course notes: The $5s\to 5p$ transition in rubidium is split into two components with wavelengths of 780nm and 795nm respectively. For the $5p$ state, ...
28
votes
8answers
4k views

Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in this video. However, I wonder; is this actually a duality? ...
3
votes
1answer
394 views

System with no entanglement but consuming quantum discord

I have come across an article which talks about quantum discord (Observing the operational significance of discord consumption. M. Gu et al. Nature Physics 8, 671–675 (2012) doi:10.1038/nphys2376), ...
5
votes
2answers
906 views

Expectation value of time-dependent Hamiltonian

I'm trying to solve a problem in QM with a forced quantum oscillator. In this problem I have a quantum oscillator, which is in the ground state initially. At $t=0$, the force $F(t)=F_0 \sin(\Omega t)$ ...
4
votes
1answer
951 views

How do I calculate the probability that the oscillator is in a certain state using partition function?

So let's say I have a single ($N=1$) quantum harmonic oscillator and the energy is determined by $E_n = (n + 1/2) \cdot \hbar \omega$ (where $n$ is the quantum number and $n$ = $0, 1, 2, \ldots$) ...
2
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0answers
101 views

What is Z3 exciton?

I am searching and studying excitons and I confronted with a term named Z3 exciton. What is it? And what is its difference with, for instance Z1 or Z2 exciton?
2
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1answer
194 views

Origin of exchage interactions

Can someone explain to me the origin of the exchange interaction between two electrically charged spin 1/2 fermions? Quantitative or qualitative accepted.
2
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2answers
653 views

Two photons of different frequencies collide to create electron and positron

A photon of frequency f, and another of frequency f' (take f' as given) collide to create an electron-positron pair. The frequency f is such that when the collision is head on, there is exactly enough ...
8
votes
4answers
2k views

What matter in the original atom bomb is converted to energy?

When an atom bomb goes off some matter is converted to energy according to $E = m c^2$. I'd like to know exactly what matter in the original atom bomb is converted to energy. Is it protons, neutrons, ...
2
votes
2answers
790 views

Can we determine whether or not a particle is entangled?

Suppose Shaniqua and Tyrone have four pairs, a, b, c, and d, of entangled particles. They take their particles and go very far apart. If Tyrone can determine whether or not a particle is still ...
4
votes
1answer
263 views

Temporal part of Quantum Wavefunction

I was hoping that someone could give me the more fundamental reason that we take as the temporal part of a quantum wavefunction the function $e^{-i\omega t}$ and not $e^{+i\omega t}$? Clearly ...
4
votes
1answer
402 views

Naive question about time-dependent perturbation theory

In time-dependent perturbation theory where $H=H_0+V$ and $V$ is considered small and has no explicit time dependence, the standard text-book treatment of the leading order probability amplitude for ...
4
votes
3answers
2k views

Canonical Commutation Relations

Is it logically sound to accept the canonical commutation relation (CCR) $$[x,p]~=~i\hbar$$ as a postulate of quantum mechanics? Or is it more correct to derive it given some form for $p$ in the ...
2
votes
3answers
196 views

Why is the planck function continuous and not discrete?

If we imagine a object made up of Hydrogen gas that is optically thick to all radiation, and is in thermal equilibrium, then, microscopically, photons will be emitted and absorbed as ...
8
votes
2answers
532 views

Wavefunction collapse and gravity

If gravity can be thought of as both a wave (the gravitational wave, as predicted to exist by Albert Einstein and certain calculations) and a particle (the graviton), would it make sense to apply ...
0
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1answer
125 views

Characteristics of bloch electron in a priodic potential

Effective mass of a Bloch electron in a periodic potential is negative why ?
5
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1answer
142 views

Order of magnetic phase transitions

Is there any phase transition occur in paramagnetism to diamagnetism transitions state. What should be the order and how will I calculate the order?
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0answers
78 views

about wavefunction and vector entries

I am beginer of physics and I am studying some very fundamental idea of quantum mechanics by myself. In the introducing book I am reading, there is an example to show a particle diffraced by a slit or ...
41
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14answers
4k views

Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
11
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3answers
1k views

Evaluating propagator without the epsilon trick

Consider the Klein–Gordon equation and its propagator: $$G(x,y) = \frac{1}{(2\pi)^4}\int d^4 p \frac{e^{-i p.(x-y)}}{p^2 - m^2} \; .$$ I'd like to see a method of evaluating explicit form of $G$ ...
8
votes
2answers
881 views

Conjugate Variables, Noether's Theorem and QM

What is the underlying reason that the same pairs of conjugate variables (e.g. energy & time, momentum & position) are related in Noether's theorem (e.g. time symmetry implies energy ...
7
votes
2answers
401 views

Is there record of a bosonic Stern-Gerlach measurement?

I cannot seem to find any peer-reviewed (or other) reference to an integer-spin Stern-Gerlach experiment. It shouldn't be too hard to do: just find you friendly neighbourhood Deuterium ion and shoot ...
9
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5answers
1k views

Why don't we use the concept of force in quantum mechanics?

I'm a quarter of the way towards finishing a basic quantum mechanics course, and I see no mention of force, after having done the 1-D Schrodinger equation for a free particle, particle in an ...
4
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1answer
348 views

Classical (or semi-classical) interpretation of photoelectric effect?

This site says that "it has recently been proven that the photoelectric effect can be interpreted classically (or at least semi-classically) in non-particle, wavelike terms". Is anyone familiar with ...
2
votes
2answers
551 views

Time evolution of a reduced density matrix

For a bipartite quantum system evolving under some master equation, is the time derivative of the reduced density matrix equal to the partial trace of the time derivative of the matrix? In other ...
1
vote
0answers
179 views

Are there any good reading materials for variational approach in many-body theory? [closed]

I need something like a summary of existing results, including the treatment of BCS Hamiltonian and Hubbard model. Auerbach's book is a good one but I still hope to get more comprehensive review. My ...
3
votes
1answer
137 views

Quantum cryptography: encryptions

I am studying quantum cryptography and I have a very basic question. Suppose A and B share a secret key k, where k=0 or 1. A wants to send one qubit to B. What A does is, if k=1, she 'flips' the qubit ...
9
votes
3answers
610 views

Derivation of the “Bethe sum rule”

I am trying to work out the steps of the proof of the expression: $$\sum_n (\mathcal{E_n}-\mathcal{E_s})|\langle n|e^{i\mathbf{q}\cdot\mathbf{r}}|s \rangle|^2 = \frac{\hbar^2q^2}{2m}$$ from Eq. (5.48) ...
18
votes
2answers
993 views

Can bosons that are composed of several fermions occupy the same state?

It is generally assumed that there is no limit on how many bosons are allowed to occupy the same quantum mechanical state. However, almost every boson encountered in every-day physics is not a ...
8
votes
6answers
1k views

What is the meaning of the word “particle” in particle physics?

I want to use Matt Strassler's definition of the word "particle" as a specific example: Matt Strassler writes: (1) "...all the elementary “particles” (i.e. quanta) of nature are quanta of waves ...
3
votes
1answer
206 views

In QM, does random data “come from anywhere”? Also, what are the properties of the data?

I have only taken a basic quantum mechanics course (this book, so you know where I'm coming from), but I've been wondering about something. If we set up a quantum system in a known state and take a ...
7
votes
2answers
218 views

Scalar product between Fock states

Suppose to have a chain (of size $L$) with bosons, and $\hat{a}_i^\dagger$,$\hat{a}_i$ are the associated creation and annihilation operators at site $i$. A Fock state can be written as: ...
3
votes
4answers
957 views

Is the momentum operator well-defined in the basis of standing waves?

Suppose I want to describe an arbitrary state of a quantum particle in a box of side $L$. The relevant eigenmodes are those of standing waves, namely $$ \left<x|n\right>=\sqrt{\frac{2}{L}}\cdot ...
0
votes
1answer
153 views

What's the proper way to approximate the position uncertainty of a particle?

In this problem: shouldn't $\Delta x\sim\lambda/\sin\theta$ be $$\Delta x\sim \frac{\lambda}{\sin\theta} - \left(\frac{-\lambda}{\sin\theta}\right) = 2\frac{\lambda}{\sin\theta}$$ instead such ...
6
votes
2answers
334 views

Meissner Effect for Type-II Superconductors

I was wondering whether the breakdown field strength for the Meissner effect may be attributed to the Zeeman effect? I can see the latter (along with the Stark effect) to be more analogous to electron ...
10
votes
1answer
5k views

Evolution operator for time-dependent Hamiltonian

When I studied QM I'm only working with time independent Hamiltonians. In this case the unitary evolution operator has the form $$\hat{U}=e^{-\frac{i}{\hbar}Ht}$$ that follows from this equation $$ ...
1
vote
0answers
86 views

Asking for references on the variational treatment of spin wave

My idea is the following: We have a system with Hamiltonian $H$, and we know that there is spin wave in this system by some symmetry-breaking arguments. Now we start from the ground state ...
1
vote
0answers
243 views

Construct the Hamiltonian of electrons on a graphene sheet ( in xy plane)

Graphene is a two-dimensional material formed by carbon atoms in a honeycomb lattice. Because of the symmetry of the honeycomb lattice, the electrons in graphene obey a linear dispersion relation ...
3
votes
1answer
360 views

Quantization of Nambu–Goto action in multiples of Planck's constant?

Isn't it possible? Quantization of Nambu–Goto action $$\mathcal{S} ~=~ -\frac{1}{2\pi\alpha'} \int \mathrm{d}^2 \Sigma \sqrt{{\dot{X}} ^2 - {X'}^2}~=~nh\qquad n \in\mathbb{Z}.$$
1
vote
1answer
141 views

Diffraction through the slit

In book "Quantum Mechanics and Path Integral", 3-2 Diffraction through the slit: Under the fig. 3-3, why did Feynman say that we cannot approach the problem by a single application of the ...
2
votes
2answers
538 views

Question on Total, Orbital and Spin Angular momentum

I am reading about the total, orbital and spin angular momentum, and I am not clear as to what these generators actually do after exponentiating. Could you give me a physical picture of what happens ...
5
votes
3answers
1k views

Does the canonical commutation relation fix the form of the momentum operator?

For one dimensional quantum mechanics $$[\hat{x},\hat{p}]=i\hbar $$ Does this fix univocally the form of the $\hat{p}$ operator? My bet is no because $\hat{p}$ actually depends if we are on ...
4
votes
1answer
639 views

Relating the variance of the current operator to measurements

(EDIT: Thanks to Nathaniel's comments, I have altered the question to reflect the bits that I am still confused about.) This is a general conceptual question, but for definiteness' sake, imagine a ...
1
vote
1answer
245 views

About Efimov States and Halo-Nuclei

I read that Halo nuclei could be seen as special Efimov states, depending on the subtle definitions. (The last sentence in the second to last paragraph of this Wikipedia article.) This does ...
0
votes
0answers
63 views

Quantum Mechanics Text for Electrical Engineers [duplicate]

Possible Duplicate: What is a good introductory book on quantum mechanics? What is a good introductory text on quantum mechanics that could be used to train electrical engineers in device ...
0
votes
1answer
308 views

Spectrum of quantum fluctuations in a harmonic oscillator

If we have a harmonic oscillator and look at it on small scale the energy is quantized and we can calculate the different eigenstates. In general the energy eigenvalues are given by $$E_n = ...
10
votes
1answer
764 views

How or why is fractional quantum mechanics important?

I read about Fractional Quantum Mechanics and it seemed interesting. But are there any justifications for this concept, such as some connection to reality, or other physical motivations, apart from ...
3
votes
1answer
129 views

Confused over the presence of 2 expressions for $\Psi(x,t)$

I'm following Griffiths' Introduction to Quantum Mechanics, and I see that he's got 2 different expressions for $\Psi(x,t)$. One of them is ...
2
votes
2answers
607 views

What's the difference between two Hydrogen atoms?

If we are given two Hydrogen atoms, would the only difference between them would be their quantum state (Energy level or eigen value, and the corresponding Orbital or eigen state) and their location ...