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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Why must $\Psi (x,t)$ go to zero faster than $\frac{1}{\sqrt{|x|}}$?

Why must $\Psi (x,t)$ go to zero faster than $\frac{1}{\sqrt{|x|}}$ as $|x|$ goes to $\infty$? According to Griffiths' Introduction to Quantum Mechanics, it must. I don't understand why, and this is ...
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Absolute value sign when normalizing a wave function

I have solved the following problem from Griffiths "Introduction to Quantum Mechanics". Consider the wavefunction: $\Psi (x,t) = A e^{-\lambda |x|} e^{-i\omega t} $ Normalize $\Psi$. Now, we ...
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2answers
355 views

Why conserved quantities in quantum mechanics are experimentally interesting?

Part of the QM lecture notes of Prof. Biswas, available online, on the harmonic oscillator reads: "Now it is easy to see from theorem 4.2 that neither P nor X is conserved. The only conserved ...
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281 views

Hardy's Theorem

https://perimeterinstitute.ca/psi_portal/sites/perimeterinstitute.ca.psi_portal/files/hardyphysrevlett.68.2981.pdf Some researchers in Bohmian Mechanics have hoped to make the theory Lorentz ...
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What's next after Higgs Boson discovery? [duplicate]

Possible Duplicate: Practical matter of the Higgs-Mechanism As everybody knows that the Higgs Boson was discovered on July 4th,2012, I am so curious about it. What are the possible ...
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How does one quantize the phase-space semiclassically?

Often, when people give talks about semiclassical theories they are very shady about how quantization actually works. Usually they start with talking about a partition of $\hbar$-cells then end up ...
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80 views

What is the minimal set of expectation values I need in a statistical model?

At least if $\vec v$ is really only a one dimensional parameter, measuring all the moments $\langle v^n \rangle_f$ seems to give me all the information to compute $\langle A \rangle_f$ with $A(v)$ ...
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694 views

Schwinger representation of operators for n-particle 2-mode symmetric states

A bosonic (i.e. permutation-symmetric) state of $n$ particles in $2$ modes can be written as a homogenous polynomial in the creation operators, that is $$\left(c_0 \hat{a}^{\dagger n} + c_1 ...
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266 views

Superposition of Electron and Positron Particle States

Let $b_k^\dagger ,b_k$ represent the creation and annihilation operators for an electron in state $k$. Let $d_j^\dagger ,d_j$ represent the same for a positron in state $j$. And let $|0\rangle$ ...
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402 views

The Dirac Equation with a 6x6 Matrix

The Dirac Equation is $$ i\hbar \frac{\partial \Psi}{\partial t}=\left[c\sum_i{\alpha_i p_i}+mc^2\beta\right]\Psi $$ with the constraints $$ \{ \alpha_i,\alpha_j\}=2\delta_{ij} \\ \{ \alpha_i, ...
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110 views

Bohmian Quantum Mechanics diffusion

About one year ago I attended a pretty interesting seminar of Nino Zanghì on the actual state of Bohmian mechanics. Now, during my undergraduate studies, I didn't have the possibility to take a class ...
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387 views

center of mass Hamiltonian of a Hydrogen atom

I'm working through Mattuck's "A Guide to Feynman Diagrams in the Many-Body Problem", but I'm stuck on a bit which I feel should be trivial. In section 3.2 (p 43 in the Dover edition) he gives a ...
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1answer
398 views

Minimizing the energy of a Slater determinant: why are the Lagrange multiplier elements of a Hermitian matrix?

If I want to minimize the energy of a Slater determinant subject to the constraint that the spin orbitals are orthonormal (as in the Hartree-Fock approximation), I can use Lagrange's method of ...
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1answer
176 views

Searching the point group of symmetry

I am engaged in the field of quantum-chemical calculations using programs written by myself. I have found out that I have a problem in finding the point group symmetry of the molecule. The first idea ...
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873 views

What does QFT “get right” that QM “gets wrong”?

Or, why is QFT "better" than QM? There may be many answers. For one example of an answer to a parallel question, GR is better than Newtonian gravity (NG) because it gets the perihelion advance of ...
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2answers
469 views

What is the relationship between distinguishability and probability in Quantum mechanics?

Firstly I am sorry for any awkward English expressions. Recently I'm reading "Feynman Lectures on Physics - Quantum Mechanics" and come to have a single question. In the book Feynman explains, "You ...
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2answers
545 views

Compton scattering angle

Say a photon hits a free electron at rest. I understand that there is a formula for the Compton scattering when the photon is scattered with an angle $\theta$, but I don't understand what determines ...
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6answers
8k views

Compton scattering vs. photoelectric effect

Say a photon hits some atom. What determines whether there will be a photoelectric effect (photon is absorbed, electron is released) or whether there will be a Compton scattering (the photon is ...
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2answers
314 views

Why Pauli exclusion instead of electrons canceling out?

To quote Wikipedia, The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions (particles with half-integer spin) may occupy the same quantum state ...
5
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1answer
330 views

Quantum spin in a rotating reference frame

Rather predictably, I'm having a hard time understanding quantum spin. I know that it has units of angular momentum and relates to rotation, but that it can't be thought of as the actual spin of a ...
2
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1answer
47 views

Will an entangled idler electron induce a current in a conductor if the signal elctron's spin is measured?

I'm assuming a hypothetical setup as follows: Two labs (Alice and Bob) exist. Each has one electron of an entangled pair. At Alice, the electron travels through free space towards a magnetic field of ...
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1answer
119 views

How would a semi-classical particle react to the double slit experiment?

As far as I know, there is a smooth transition between quantum and classical regimes, so that even classical particle like a massive object has a wavefunction associated with it. However, the double ...
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1answer
140 views

Can entanglement be used to decrease entropy of two systems?

I know that entanglement can create correlation between systems. Would it be true to say that entanglement create constraints between systems? Can constraints be used to lower the total entropy of ...
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501 views

How can a particle with no size have angular momentum?

I was recently reading about Higgs boson and particle spin and I stumbled upon a question that explains what is spin. It explains that electrons have no size yet they have angular momentum. I don't ...
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1answer
207 views

Why don't cancelling wavefunctions for two different particles give zero total wavefunction?

Let $\left|a\right>=e^{i(kx-\omega t)}$, $\left|b\right>=-e^{i(kx-\omega t)}$ be two neutral particles in the 1D free space without any interaction. Then ...
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What does it really mean that particle has a spin of up/down? And how is spin actually meassured?

I been reading some physics articles (related to the recent discovery of the particle that could be a Higgs boson) posted online and it was talking about electron spin and how it can only have values ...
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221 views

How can a pion have a mass, given it's a “field mediator” and created/destroyed continuously?

Maybe some of my assumptions here are basically wrong, but isn't it true that pion is the "mediator" for the strong force field. the quantum field theory basically says that there are no fields, ...
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2answers
209 views

Motivation for “discretized quantum state spaces”

I know that the title of the question is rather vague, so let me clarify what I mean. For a quantum system, the set of states has infinitely (even continuously) many extreme points, i.e. there are ...
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1answer
652 views

Does a spin-2 particle really return to its previous state after 180° rotation?

It is often claimed that spin-2 particles return to their previous state after $\pi$ rotation, just like spin-1/2 particles return after $4\pi$ rotation. But my calculation suggests otherwise. Let z ...
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3answers
2k views

Expressing a unitary operator in terms of a Hermitian operator

In the context of unitary transformations as a change of basis in Hilbert space, Gottfried and Yan wrote in their book on quantum mechanics that expressing a unitary operator $U$ in terms of a ...
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3answers
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Quantum levitation (locking) 3mm thick disk could carry 1000kg small car claim

I watched this TED presentation: http://www.ted.com/talks/boaz_almog_levitates_a_superconductor.html It is about superconductivity and quantum levitation. It tells that super-thin, three-inch disk ...
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Why are there only perfectly anti-correlated quantum states, not perfectly correlated?

The singlet state of two qubits is anticorrelated in every basis. For example, in the Pauli bases, it can be expressed, $\frac{1}{\sqrt{2}} ( | 01 \rangle - | 10 \rangle) = \frac{1}{\sqrt{2}} ( | +- ...
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315 views

Does the wave nature of a particle refer to the wave function?

In quantum mechanics when we talk about the wave nature of particles are we referring in fact to the wave function? Does the wave function describes the probability of finding a particle (ex: ...
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1answer
141 views

Is it possible to send a single photon from a distant planet (say Mars) and detect its arrival at a site on Earth?

My question is specifically whether there exists a technique by which a single photon can be "tagged" or "encoded" in such a way that it can traverse our atmosphere and arrive at some sort of detector ...
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374 views

Superposition of Negative and Positive Energy States

This is a question about the negative energy solutions to the free particle Dirac Equation in the first quantized picture. We need both the positive and negative energy solutions to have a complete ...
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3answers
361 views

Extending mixed states to pure state

Let us consider any pure state $|\psi\rangle\in\mathbb{C^n\otimes C^n\otimes C^n}$. Its reduced bipartite density matrix represent a pure state or mixed state depending on whether $|\psi\rangle$ is ...
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3answers
226 views

Misconception about the expectation of a quantum system

For a two-level quantum system with energy eigenstates $|\phi_1\rangle$ and $|\phi_2\rangle$ at finite temperature, we can write a general state as ...
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2answers
214 views

Batting averages of the Large Hadron Collider

As I understand it, the Large Hadron Collider's function is to throw particles into each other while avoiding hitting the nucleus? If quantum mechanics dictate the position of a particle can only ...
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1answer
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Existence of quantum computer

At time there are talks about quantum computers and lot of talks and discussion on its exponential speed. But studying in some more details it makes reference to "Heisenberg uncertainty principle", ...
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331 views

Properties of expectation values of quantum operators [closed]

$$\langle \hat A \rangle \langle \hat B \rangle=\langle \hat A\hat B \rangle,$$ $$\langle \hat A \rangle + \langle \hat B \rangle=\langle \hat A + \hat B \rangle,$$ $$\langle \hat A^2 \rangle ...
2
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4answers
255 views

Non linear QM and wave function collapse

I heard that there have been some propositions about describing the collapse of the wave-function by adding non-linear terms, but I couldn't anything in any any textbooks or even articles (probably ...
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4answers
4k views

What is meant by “Nothing” in Physics/Quantum Mechanics(QM)?

I am not a phycisist, so please forgive my ignorance. This is related to my posts and this. I am trying to undertand what is meant by the term "Nothing" in physics or Quantum Mechanics since it seems ...
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2answers
733 views

Naive question on quantum mechanics and uncertainty principle

This is a follow up on this question, the answer of which points towards Quantum Mechanics. As stated I am not a phycisist so please forgive my ignorance. I will try to understand the issue by going ...
2
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1answer
479 views

Magnetic moment derivation from Dirac equation

I am reading a text book where they show the electron has spin 1/2 using Dirac's equation. At one point in the derivation they define $\pi=P-qA/c$ where $P$ is the momentum operator and A is the ...
2
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2answers
105 views

Is there any correlation between the energy density fluctuations of two separate systems in a vacuum state?

I think the title says it all. What I am curious to find out is if there are any observable changes in the fluctuations of zero-point energy in a vacuum state system that are the consequence of ...
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What keeps electrons in an atom from flying away or falling into the nucleus?

In atoms, what force or charge, etc. keeps electrons from flying away or into their nucleus? is there a kind of weak-force at work on the atomic scale? Note I am aware the electron positions are ...
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3answers
106 views

Can two distinct spatially separated many-body systems in the ground state contain entangled particles?

In particular, I am asking if two distinct many-body systems (e.g. system A and system B) separated at some arbitrary distance will necessarily be found to contain entangled particles (such that ...
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Natural macroscopic amplification of quantum randomness [closed]

What are some good examples? For example, chaotic systems where you can show that quantum nondeterminism sets the initial conditions.
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472 views

What happens in this revised double-slit experiment?

Put the classical electron-emitting double-slit apparatus in a sealed box. At each slit there's a counter to check whether an electron has passed it or not, so had the apparatus been left in open, we ...
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245 views

Is it possible to create an entangled pair of photons if they originate initially from operations at two separate sites?

My question is whether or not it would be possible to create an entangled state between two photons that do not share the same initial photon source and their respective sources are separated by an ...