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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8
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2answers
792 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
346 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
votes
5answers
965 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
votes
1answer
317 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
505 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
178 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
134 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
557 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
888 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
203 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
213 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
901 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
298 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 ...
7
votes
1answer
5k views

Evolution operator for time-dependent Hamiltonian

When i studyed QM I'm only working with non time-dependent Hamiltonians. In this case unitary evolution operator has the form $$\hat{U}=e^{-\frac{i}{\hbar}Ht}$$ that follows from this equation $$ ...
1
vote
0answers
84 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
230 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
321 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
126 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
517 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
739 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
583 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
227 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
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0answers
62 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
290 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
708 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
531 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 ...
4
votes
1answer
247 views

Probability in Quantum Mechanics

Do you need to take a probability/statistics course for Quantum Mechanics, or is the probability in quantum mechanics so rudimentary that you can just learn it along the way? I'm in doubt as to ...
-1
votes
1answer
197 views

Direct nuclear reactions problems [closed]

can anyone explain Multi-step nuclear reactions in terms of direct nuclear reactions .
0
votes
1answer
272 views

Direct nuclear reaction in nuclear physics

Time taken to occur a direct nuclear reaction is very low $10^{-22}$sec . I want to know the Importance of direct nuclear reactions.
5
votes
1answer
223 views

Hawking Radiation from the WKB Approximation

Reading this paper which is itself an exposition of Parikh and Wilczek's paper, I get to a point where I fail to be able to follow the calculation. Now this is undoubtably because my calculational ...
2
votes
1answer
733 views

What is different between resolvent and green function

I bumped into a book, where Resolvent $R^{\pm}(E)$ is defined as $e^{\mp iHt/\hbar}=\pm\frac{i}{2\pi}\int_{-\infty}^{\infty}dER^{\pm}(E)e^{\mp iEt/\hbar}$ and $R^{\pm}(E)=\frac{1}{\pm ...
5
votes
1answer
2k views

Momentum as Generator of Translations

I understand from some studies in mathematics, that the generator of translations is given by the operator $\frac{d}{dx}$. Similarly, I know from quantum mechanics that the momentum operator is ...
3
votes
1answer
278 views

Hubbard Model Hamitonian

$H = -\sum\limits_{i,j} A_{ij} c_i^{\dagger} c_j + \frac{U}{2} \sum\limits_i(c_i^\dagger c_i)(c_i^\dagger c_i -1)$ is defined to be a Hamiltonian for modeling quantum random walk of identical ...
1
vote
4answers
865 views

Hamiltonian in position basis

Let $ H = \frac{-h^2}{2m}\frac{\partial^2 }{\partial x^2}$. I want to find the matrix elements of $H$ in position basis. It is written like this: $\langle x \mid H \mid x' \rangle = ...
7
votes
1answer
452 views

The cleverest way to calculate $\left[\hat{a}^{M},\hat{a}^{\dagger N}\right]$ with $\left[\hat{a},\hat{a}^{\dagger}\right]=1$

Who can provide me some elegant solution for $$\left[\hat{a}^{M},\hat{a}^{\dagger N}\right]\qquad\text{with} \qquad\left[\hat{a},\hat{a}^{\dagger}\right]~=~1$$ other than brute force calculation? ...
7
votes
3answers
439 views

An electron falling into a black hole

If an electron falls into a black hole. How can the Heisenberg uncertainty principle hold? The electron has fallen into the singularity now so it has a well defined position which means that it ...
4
votes
4answers
10k views

Can an electron be in two places at the same time?

So I've been reading a bit and watching some videos about the double slit experiment, and therefore the wave particle duality; I've also read this "implies" that a particle can be in two places at the ...
4
votes
3answers
267 views

Irreversibility and the Fermi golden rule

When a quantum system is perturbatively coupled to a continuum of states, one uses the Fermi's golden rule to compute the rate of transition form an initial state to a set of states contained in an ...
5
votes
4answers
3k views

Help an aspiring physicists what to self-study [closed]

This is probably not the kind of question you'll often encounter on this forum, but I think a bit of background is needed for this question to make sense and not seem like a duplicate: 2012 has been ...
2
votes
2answers
835 views

What is the real interpretation of Planck's constant and what are its origins?

In the physics texts I have read and from other online information, I gather that Planck's constant is the quantum of action or that it is a constant specifying the ratio of the energy of a particle ...
1
vote
1answer
406 views

Why do the drift and diffusion components cancel for each type of carrier if EHP generation plays such big role in p-n-junctions?

I have always argued to myself that drift and diffusion components of the current though a p-n-junction cancel for each type of carrier because any electron diffusing from n into p will sooner or ...
8
votes
5answers
687 views

Born rule and unitary evolution

Is the Born rule a fundamental postulate of quantum mechanics, or can it be inferred from unitary evolution?
0
votes
1answer
134 views

How to go from Quantum World to Classical World? [duplicate]

Possible Duplicate: Is it possible to recover Classical Mechanics from Schrödinger’s equation? Classical Limit of the Feynman Path Integral In the quantum world we don't have ...
1
vote
1answer
103 views

Isn't it incorrect for the minimal gauge coupling and related calculations in Prof. Ezawa's book on quantum Hall effect?

He is CORRECT. I use $\mathbf{B}=\left(0,0,B_{\perp}\right)$ and he use $\mathbf{B}=\left(0,0,-B_{\perp}\right)$. $B_{\perp}>0$. Nov.28.2012 Basically I got mad with conventions. 1.Here is the ...
1
vote
2answers
989 views

What does the general solution of the Schrodinger equation represent for the particle in a box problem?

For the particle in an infinitely deep potential well, I have an intuitive picture of the separable solutions of the Schrodinger equation as being the wavefunctions for the different allowed energy ...
-1
votes
1answer
197 views

About interchange phase of identical particles in Weinberg's QFT book

In Weinberg's textbook on QFT(google book preview), he discussed the phase acquired after interchanging particle labels in the last paragraph of page 171 and the footnote of page 172. It seems he's ...
7
votes
2answers
398 views

Scattering states of Hydrogen atom in non-relativistic perturbation theory

In doing second order time-independent perturbation theory in non-relativistic quantum mechanics one has to calculate the overlap between states $$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' ...