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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39 views

Increase path length for a photon with two mirrors vs optical fiber

Is it possible to build two mirrors in vacuum such that a light pulse (single photon) gets refleted many times in order to increase the distance it travels? For example like that? Say I want the ...
2
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2answers
54 views

What happens at the subatomic level when energy is added to an atom?

For the sake of simplicity I shall use the hydrogen atom. I know that adding energy to the hydrogen atom means bombarding it with photons. I am curious about what happens to the quarks and electron of ...
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2answers
60 views

Stability of the hydrogen atom and positronium

I am trying to get a better understanding of why positronium decays while a hydrigen atom is stable. In the case of positronium, I can write an elementary process were the leptons annihilate into two ...
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0answers
62 views

When is Fermi golden rule exact?

My recent study Nonsmooth and level-resolved dynamics illustrated with a periodically driven tight binding model motivates me to ask this question: Is there any example in which the Fermi golden rule ...
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0answers
44 views

Size of an elementary particle [duplicate]

Do we have a well defined mathematical expression denoting the size of a fundamental particle with no internal structure (electron for example) ? If we do, how does it fit in with the uncertainty ...
2
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0answers
49 views

Quantum Mechanics and Direction of time [duplicate]

It always fascinate me that time is symmetrical classical physics while in life we all experience flow of time in only one direction. There is no preference direction of time in classical physics. The ...
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1answer
66 views

Double-slit-experiment but with unobserved alternating opening of slits. Does an interference pattern still arise?

Step #1 Imagine one preforms an electron based Double-slit-experiment and one does so with only one electron being fired at a time. Step#2 Also included in the experiment is an unobserved ...
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0answers
18 views

Could symmetric molecular stretching cause a physical object to become amorphous? [closed]

I understand very little of this, but my google-foo has yielded me next to nothing, I thought I might then just ask. My real question here is if it might be possible through the use of vibration to ...
2
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2answers
69 views

Eigenstates of a shifted harmonic oscillator

Let's say I have a quantum harmonic oscillator $H = \omega a^\dagger a$, where $a^\dagger$ is the raising operator and $a$ is the lowering operator and $H |n\rangle = \omega n |n\rangle$. Now assume ...
3
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1answer
58 views

Where does either Bohr or Heisenberg mention the idea of the wave function collapsing?

Could someone reference a paragraph written either by Heisenberg or Bohr where they mention the idea of the wave function collapsing?
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1answer
50 views

Jahn-Teller effect is based on the Born-Oppenheimer approximation?

I am now reading the quantum mechanics textbook by Landau and Lifshitz. In section 102, they discuss the Jahn-Teller effect. It seems that they assume the Born-Oppenheimer approximation. There is ...
2
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1answer
43 views

Is WKB really applicable for the ground state?

It is a long time question for me. For me, it seems that WKB is applicable for a given $E$ if and only if $\hbar$ is sufficiently small. Or in other words, WKB is applicable if and only if the ...
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2answers
53 views

Question on the logical structure of the EPR argument and Bell's inequalities

Recently I have read a lot online about the EPR argument and Bell's inequalities and its implications. When comparing what people write there online with the actual research articles of Einstein and ...
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1answer
288 views

Relationship between Schrodinger equation and string/membrane

In Sakurai's Modern Quantum Mechanics (2nd ed) p.99, he says We know from the theory of partial differential equations that (time-independent Schrodinger equation) subject to boundary ...
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0answers
40 views

Ladder operator notation?

If I have the ladder operator $D(AB)$ which is a lowering operator, where $D(AB)=D(A)+D(B)$ does the things in the brackets e.g. AB indicate what wave function this operator applies to, i.e. is the ...
1
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1answer
71 views

Derivation of $a_{j}$ coefficients in the quantum harmonic oscillator

In Griffiths' book page 53, when we derive the solution of the quantum harmonic oscillator by using the power series way, we have: $$a_{j+2} = \frac{2j+1-K}{(j+1)(j+2)}\, a_{j} .$$ And for large $j$, ...
6
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2answers
2k views

Where does the number “380,000 years for electrons to be trapped in orbits around nuclei” come from?

How does this number get calculated? About 380,000 years after the Big Bang the temperature of the universe fell to the point where nuclei could combine with electrons to create neutral atoms. ...
1
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1answer
47 views

Is there a standard resource that lists all understood particle-particle relationships?

I am just starting to dig a little deeper into particle interactions, and just have an introductory college physics background (no quantum mechanics). But I am interested in the conditions of the ...
2
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4answers
87 views

What exactly is meant by “observed” when talking about the wave-particle duality?

When talking about the wave-particle duality, teachers and books say that when you send a single photon through a slit, it makes a wave pattern. But if you send that particle through the slit and "you ...
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1answer
62 views

Spin-½ and beyond: Measuring spin components other than ± ħ / 2: How to formulate the probability function?

It is my understanding that in quantum mechanics (for 1/2 spin particles) the probability function that describes the direction of a particle's spin state is proportional to the overlap of the ...
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3answers
225 views

Interpretation of the wave function in quantum mechanics

I just started watching the coursera lectures on the basics of quantum mechanics and one of the first lectures were on deriving Schrodinger's equation and its interpretation it under Born's ...
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0answers
44 views

Theoretically, is there a way to hold a quantum entangled particle in a state by continuously observing it?

When the spin of a quantum entangled particle is measured, is it only possible to do an instantaneous measurement, or can a particles spin be held in a collapsed state by constantly observing it? In ...
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0answers
25 views

Study Basic Quantum Mechanics [duplicate]

What is the appropriate mathematical background someone must attain in order to enroll in a quantum physics course for beginners?
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5answers
416 views

Differences between probability density and expectation value of position

The expression $\int | \Psi\left(x\right)|^2dx$ gives the probability of finding a particle at a given position. If wave function gives the probabilities of positions, why do we calculate ...
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1answer
26 views

Variable definition in wave function for scattering particle?

For the wave function of a scattered particle when finding the scattering aptitude we have: $$\psi(r)=Ae^{ik_0∙r}+\frac{2\mu}{\hbar^2} ∫G(r-r')V(r')\psi(r')d^3r'$$ I was wondering what the variables ...
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1answer
77 views

Perturbation theory emitting high order powers

For my second-order energy correction for a harmonic oscillator in an electric field I have the following: $$q^2\varepsilon^2\sum_{m\neq n}\frac{|\langle m|x|n\rangle|^2}{E^{(0)}_n-E^{(0)}_m}+\text{ ...
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0answers
37 views

How do I calculate integer and half integer spin? [closed]

How do I calculate integer and half integer spin, and how do I use the calculations?
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1answer
57 views

Why are atomic quadrupole moments calculated using nuclear spin?

It's my understanding that electric quadrupoles interact with the gradient of an electric field, and I understand roughly how this works. I am trying to calculate the interaction between an atomic ...
1
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1answer
63 views

The role of SO(3) and SU(2) in quantum mechanics [duplicate]

When studying the irreducible representations of SO(3) one usually looks at the irreps of the infinitesimal rotations instead, i.e. the ones of so(3), the Lie Algebra of SO(3). The Irreps of so(3) can ...
4
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4answers
134 views

Why do we look at the representations of $SO(3)$ in QM?

I have a bit of an understanding issue why the representations of $SO(3)$ are so important for Quantum Mechanics. When looking at its Irreps one gets the Spin and Angular Momentum operators and thus ...
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1answer
40 views

Symmetric eigenfunctions?

So a symmetric eigenfunction / wavefunction is defined as: $$P_{ij} ψ_a (r_1,r_2,…,r_i,…,r_j,…,r_N )=ψ_a(r_1,r_2,…,r_i,…,r_j,…,r_N )$$ But for it to be symmetric does this have to be true for all $ij$ ...
3
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1answer
174 views

Neil deGrasse Tyson says that electrons “teleport” between energy levels?

This page: https://blog.afach.de/?p=62 Discusses the error Neil deGrasse Tyson made when talking about electronic transitions (video included there). Tyson clearly said in his Cosmos series that ...
3
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1answer
72 views

Inner products containing the tensor product of two operators

The book Nielsen & Chuang "Quantum Computation and Quantum Information" presents the concept of tensor products as follows. Suppose we have the vectors $|v\rangle$ and $|w\rangle$ which exist in ...
6
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2answers
977 views

Can I steal your electron?

The following paragraph has been extracted from the Wikipedia (Atomic orbitals): Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the ...
4
votes
3answers
419 views

Classical analogue of Heisenberg and Schrödinger pictures?

What do the Heisenberg and Schrödinger pictures in quantum mechanics correspond to in classical mechanics (if they correspond to anything)? It's kind of weird, because (if I understand it well) in ...
1
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2answers
60 views

Quantum computing and ambiguity

I do a bit of hobby programming and I often search the internet for little oddities that are fun to ponder over. I have read a few passages that try to explain quantum computing to the layman like ...
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0answers
32 views

Why does proton and electron attract each other? [duplicate]

Not that their charges are opposite! "+" & "-" are the signs we named them. By nature Why do they attract each other? And Why do they repel each other?
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2answers
55 views

Why do rotations of a multicomponent state function take this form?

I am reading Leslie Ballentine's Quantum Mechanics, section 7.2, which is all about the explicit form of the Angular Momentum operators. I understand how he gets the form for the single component ...
3
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1answer
57 views

Normalising a wave function in parts?

If we have the wave function $\psi_{100}(r,\theta,\phi)=R_{10}(r)Y_{00}(\theta,\phi)$ when we are normalising it we do the following: $$1=\int| \psi_{100}(r,\theta,\phi)|^2sin(\theta) r^2drd\theta ...
1
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0answers
90 views

Link between Quantum and Classical Mechanics [duplicate]

In classical mechanics we have momentum as generator of translation by following definition: $$f(x+\delta x)=f(x)+[f(x),p]\delta x+....$$ I was wondering whether using this relation and commutation ...
1
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0answers
31 views

Books on foundations of QM [duplicate]

I am seeking for books on foundations of Quantum Mechanics with subjects like the EPR experiment, Bell's theorem, the problem of measurement, entanglement, decoherence, nonlocality, interpretations, ...
6
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6answers
413 views

Electron shells in atoms: What causes them to exist as they do?

I have seen similar posts, but I haven't seen what seems to be a clear and direct answer. Why do only a certain number of electrons occupy each shell? Why are the shells arranged in certain distances ...
2
votes
3answers
71 views

What does the $y$-axis represent in the atomic spectra and what is its significance?

The picture is an emission spectrum of Helium. The spectrum has sharp lines (peaks) at certain wave lengths characterizing it as helium. Agreed that it characterizes Helium as atomic spectral line ...
0
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2answers
55 views

Differentiation operator with respect to observable acting as a function of the observable?

In his Principles of Quantum Mechanics Dirac writes: $$\int \langle \phi \frac{d}{dq}|q'\rangle dq' \psi(q')=\int \phi(q') dq' \frac{d\psi(q')}{dq'}.$$ To me it is rather strange, and it seems as if ...
4
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1answer
77 views

If virtual particles have negative mass why do they contribute positive mass to atoms?

According to Lawrence Krauss, atoms containing in our body consists of merely 10% (if I remember correctly) of our total mass. The rest come from virtual particles popping in and out of existence from ...
2
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1answer
70 views

Amateur thoughts on QM theory at celestial scale

Some amateur scientist asked me that why can't one just simply apply the entire theory of QM at atomic scale to "quantize" celestial system with a different choice of $\hslash$, which he believed can ...
0
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2answers
95 views

Quantum Mechanical States

What can be the precise answer to the question that Quantum states are complex and infinite dimensional. Why is this so? Is it because they belong to the complex Hilbert space? Even if they ...
6
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1answer
45 views

Is the subadditivity of quantum entropy valid in the infinite-dimensional case?

Does the subadditivity (and strong subadditivity) of quantum entropy hold for infinite dimensional quantum systems as well? Unfortunately the books in my hand give proof for finite dimensional cases ...
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2answers
111 views

Why are results of Bell's experiments considered to “break realism”?

Related to my previous question (Why would classical correlation in Bell's experiment be a linear function of angle?), as a newbie in quantum mechanics, I am also unable to find the reason to why ...
3
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0answers
62 views

Why do people say “Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon).”?

Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon, etc.). I read this in a paper (version1 of http://arxiv.org/abs/1404.3728v1, 1st page 1st ...