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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81 views

What is the difference between correlation and entanglement?

I have read that not all correlated states are entangled. What is the difference between the two? Mathematically, it was stated that a system which can be put in the form of ...
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55 views

Hamiltonian for Electron in Magnetic Field with Symmetric Gauge in Polar Coordinates

I am new on the board and have a question about how to write the Hamiltonian for an electron in a magnetic field rotating at a fixed radius. I would like to write the hamiltonian using the symmetric ...
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1answer
134 views

Can Bell's inequality violation be explained by the will of the scientist somehow affecting the experiment?

As far as I know, there are three possible ways to explain violation of Bell's inequality: violation of realism, violation of locality and violation of freedom. The first two are pretty ...
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2answers
360 views

What is meant by the spin of a particle? [duplicate]

I have been studying that electrons have quantum number called spin quantum number(s), this number can have either +1/2 or -1/2 value. If s=+1/2, the spin is clockwise and if s=-1/2, the spin is anti ...
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2answers
87 views

What does $g^{(2)}$ signify in quantum optics? And how to calculate it?

I have been studying research papers on Quantum Optics and non-linear optics. I frequently come across the $g^{(2)}$ value. What does it signify? What is its importance? How to calculate it? And ...
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1answer
45 views

Have $2s_{1/2}$ and $2p_{1/2}$ the same energy?

I have always known that p-states are more energetic than s-states. But in this picture I see the following: And it confused me. Could anyone explain if both levels have the same energy?
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74 views

Domain of simple quantum harmonic oscillator

When discussing the spectral theory of unbounded operators, one often starts with an operator defined on a densely defined subspace of your Hilbert space, and then proves that the operator is ...
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59 views

Use a Delayed Choice Quantum Eraser to communicate Faster Than Light [duplicate]

In the experiment setup picture of the Delayed choice quantum eraser, photons reach D0 and shows a pattern, before its quantum entangled counterparts reach one of D1, D2, D3, or D4. The pattern ...
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68 views

What causes Paulis Exclusion Principle?

Currently I'm taking an astrophysics class and has now come across electron degeneracy. As far as I understand, the reason why white dwarfs and such, does not collapse, is due to this, meaning that ...
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41 views

The electron: why can't it have both momentum and position [duplicate]

Total amateur here. I've been watching video lectures on Quantum Mechanics and it's said that there is no way to know both position and momentum of an electron at the same time. But is it because when ...
4
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1answer
137 views

Why is Planck's constant the same for all particles?

This question came to me while reading "Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from?". This question has a nice answer that explains that wave number has be ...
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18 views

Can anyone give me a simple proof for the sign change of electronic wavefunction when taken around a loop containing a conical intersection?

How and why does the sign of the electronic wavefunction changes when it is taken around a contour? For example, suppose the initial wavefunction is $f(s;S_0)$ at nuclear configuration $S_0$ and now ...
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2answers
75 views

Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from?

I'm curious where the expression $p=\frac{h}{\lambda}$ comes from. I know that for light, the following is true: $E=pc$ and $E=hf$ so, $pc=hf \Rightarrow p=\frac{hf}{c}=\frac{h}{\lambda}$ But how ...
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1answer
43 views

How to understand the unitary? [closed]

In the page 219 of Mahan's Many Particle Physics(3ed), there exists a transform $$ S=c^{\dagger}c\sum_q\frac{M_q}{\omega_q}(a_q^{\dagger}-a_q)$$ In order to prove that the transformation relating to ...
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3answers
196 views

Why particle number operator $\hat{N}$ is $\hat{a}^\dagger\hat{a}$ rather than $\hat{a}\hat{a}^\dagger$?

Both $\hat{a}^\dagger\hat{a}$ and $\hat{a}\hat{a}^\dagger$ are Hermitian, how do we know which one represents the particle number?
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13 views

Split property for type III algebras entails practical separability

I am reading Halvorson's thesis (http://philsci-archive.pitt.edu/346/1/main-new.pdf), however I don't understand a proof at p.50 where he tries to explain why the split property allows a local agent ...
4
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1answer
67 views

Where is quantum physics with regards to the periodic table?

In his Lecture's on Physics (circa 1960's) Richard Feynman wrote that so far physics has only been able to model (solve) the hydrogen and helium atoms. So now, more than 50 year's later where are we ...
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1answer
43 views

Question about one of the problems of the Bohr model

This is probably extremely basic physics that I don't know, but I'm still going to ask: Say in hydrogen, according to the Bohr model the electron is "really" orbiting the proton, and as a consequence ...
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1answer
140 views

Can an electron stand in place of proton like a ghost standing in place of you?

The atomic orbital refers to the physical region where the electron can be calculated to be present, as defined by the particular mathematical form of the orbital 1. The picture below shows the $1s$ ...
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2answers
54 views

Does quantum mechanics contradict macroscopic determinism?

I am wondering whether it is true to ask whether determinism is still completely viable at macroscopic scales given that the constituent particles behave according to QM when the dimensions get small ...
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0answers
14 views

Wave-like description of Compton scattering and photoelectric effect

I have found in the wikipedia page for QFT the following statement: ... Although the photoelectric effect and Compton scattering strongly suggest the existence of the photon, it is now understood ...
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56 views

Interesting (new to me) things in the exposition of Landau's book on QM

In section I.1 (The uncertainty principle), a principle I already know, the author suggests a "relaxing" picture (Unusual): "We have defined "apparatus" as a physical object which is governed, ...
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1answer
43 views

What is a Hulten potential?

What is the Hulten potential? When is it used? How is it derived? I vaguely heard about in the context of neutron synthesis / quantum mechanics. thanks
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2answers
95 views

Understanding basic quantum mechanics notation

I was talking with a guy about energy levels of an atom in a magnetic field. He said that energy levels are shifted and that, if you want know how much, you have to analyze this: for 1s state: ...
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1answer
77 views

How does vacuum state look in first quantization?

Wikipedia says that the vacuum state is the unit of tensor product. In my understanding then, a first-quantized wavefunction for the vacuum state would be just constant in the each particle's ...
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1answer
32 views

How did phase randomly changed in CHSH test (M. A. Rowe and others)?

Measuring phase of photon should always be randomly changed while checking CHSH inequality, but i can't explain this: http://qudev.ethz.ch/content/courses/QSIT08/pdfs/Rowe01.pdf (the most clear ...
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69 views

Is it possible that we have a physical state which is a mixture of discrete eigenstates and continuous ones?

For a system has both continuous and discrete spectrum, is it possible that a physical states is something like: ...
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1answer
29 views

Why the first Term is higher in energy than the second?

P. W. Atkins writes in his book "MOLECULAR QUANTUM MECHANICS" in section 9.4 "Term symbols and spectral details" "We shall adopt the convention that the first term is higher in energy than the ...
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1answer
46 views

Expectation value of $a_i^\dagger a_i$ for thermal density matrix

Suppose we have some heat bath with Hamiltonian, $$H=\sum_n \left(a^{\dagger}_na_n+\frac{1}{2}\right)\hbar\omega_n$$ and a density matrix $\rho=Z\exp(-\beta H)$ for some normalisation $Z$. ...
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45 views

What does the wavefunction actually show?

I.e. when someone says they've solved the Schrödinger equation for something, or that the equation can be used to show how the wave function develops over time, what do they mean? I know that its to ...
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1answer
77 views

$\sigma$-additivity of Probability and Quantum Mechanics

$\sigma$-additivity - probability of a sum of countable number of pairly disjoint events equals a sum of probabilities of these events. (3. Axiom of Probability) For pairly disjoint sets $A_k$ ...
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1answer
25 views

The expectation value of the spin of a proton which is entangled

Suppose we have the Bell state $$|\text{ }\psi\rangle=\frac{1}{\sqrt{2}}\left(|\uparrow\rangle_1|\downarrow\rangle_2+|\downarrow\rangle_1|\uparrow\rangle_2\right)$$ and denote the spin operator of the ...
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2answers
74 views

What's the difference between hopping and tunneling?

My professor made a distinction between electron hopping (the closest wikipedia had an article on) and tunneling, saying that one (he didn't say which, but I assume hopping) was temperature dependent ...
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3answers
73 views

Is the uncertainity principle a practical reality, a theoretical law or a measurement problem?

I understand we cannot state with arbitrary precision the position and momentum of a micro-particle as we superpose infinite waves to create a wave packet at the exact position of the particle and ...
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1answer
71 views

How to choose the Correct Green's Function?

In order to solve the Green’s function of the Helmholtz operator $$(\nabla^2+k^2)G(\vec r-\vec r’)=\delta^{(3)} (\vec r-\vec r’)$$ one can obtain four different Green’s functions corresponding to four ...
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7answers
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Does electron being many places at the same time violate Physics laws?

The following passage has been extracted from the book Parallel Worlds, by Michio Kaku: Because of uncertainty, the electron does not exist at any single point, but exists in all possible ...
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3answers
186 views

How to derive $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$

Wikipedia indicates that the following relation is "easily shown": $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$, however I'm having some trouble showing it. I think I'm just ...
2
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3answers
161 views

What is the best article presenting counterarguments to a many-world interpretation? [duplicate]

I'd like to see a clear overview of why the many-world interpretation (WWI) of quantum is wrong, written by someone who believes that. This would be aimed at a technically aware audience, yet as an ...
2
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3answers
80 views

Intuition on positive-operator valued measures (POVM)

I'm having a little trouble understanding what positive-operator valued measure (POVM) are- in particular why/how they are non-negative. For instance, if they just represent measurements, what about ...
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3answers
51 views

Is a gapless system always conducting and a gapped system insulating?

In an answer to this question, @user566 mentioned that there is a qualitative difference between gapped and gapless systems; that gapless systems are conducting and gapped system are insulating. Is ...
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0answers
38 views

Wigner function for position eigenstates

What is the Wigner function (or $P$ or $Q$ function) associated with $|x\rangle\langle x|$? Thanks for any suggestion.
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2answers
106 views

Particle in a Box: Energy Less than the Potential Energy

I am reading quantum mechanics from Shankar's Principles of Quantum Mechanics. On page 157 he defines the box potential $V(x)$ as $$ V(x) = \left\{ \begin{array}{rl} 0 &\mbox{ if $|x|< L/2$} ...
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1answer
46 views

How can an electron be fired at a target when uncertainty principle says it will spread out around axis of motion?

Consider an electron fired at a target. Taking the axis of motion to be $x$, and position to be $(x,y,z)$ then $\Delta y = \Delta z = 0$ Therefore by the uncertainty principle $\Delta p_y = ...
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0answers
27 views

Quadrupole moment of a valence proton

The state of an unpaired nucleon in the nuclear shell model is given by the quantum numbers $l$, $s$, $j$ and $m_j$ resulting from coupling $l$ and $s$ when we add spin-orbit interaction. In chapter 5 ...
1
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1answer
42 views

Why does Fermi level has a probability density of 1/2 while it may lie in the forbidden region?

I dont understand how there is a continuous probability density function in semiconductors, when there are several regions which are restricted by Energy, i.e. forbidden energies. Well i know that in ...
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29 views

What are the “name” and “coname” of operators?

So, I've been reading articles about categorical quantum mechanics, and I keep coming across definitions of "name" and "coname" of an operator. Googling these basically only turn up the papers I've ...
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2answers
90 views

What does volume means at the quantum level?

The volume of the electron is the space bounds in which it is contained says the @CuriousOne. But how can we define the volume in such a small range. If we immerse a cuboid into a vessel full of ...
2
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1answer
77 views

Why does Dirac write $\langle\xi'|\overline{f(\xi)} = \overline f(\xi ')\langle\xi'|$?

Starting on page 41 of Dirac's The Principles of Quantum Mechanics, he defines $f(\xi)$ in general to be that linear operator which satisfies $$f(\xi)|\xi'\rangle = f(\xi')|\xi'\rangle\tag {34}$$ ...
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1answer
110 views

Quantum harmonic oscillator solved by analytic method using Schrödinger equation and wave function

I'm having trouble understanding the recursion formula. Using $\xi \equiv \sqrt{m\omega/\hbar}x$ and $K = 2E/\hbar\omega$, the time-independent Schrödinger equation becomes $$\frac{d^2\psi}{d\xi ^2} ...
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4answers
654 views

Why do electrons in an atom occupy only the stationary states?

When we talk about the elementary problems in quantum mechanics like particle in a box, we first calculate the energy eigen-function. Then we say that the most general state is the linear combination ...