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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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 ...
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1answer
49 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 ...
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1answer
56 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 ...
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2answers
86 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 ...
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1answer
38 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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1answer
69 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 ...
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3answers
105 views

Angular momentum eigenstates

My textbook says that if $L^2$ is the square of the angular momentum and if it's eigenstate is $|\alpha,\beta>$ then its eigenvalue is $\hbar^2\alpha$ i.e. ...
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1answer
154 views

What does the magnetic field of the (quantum-mechanical) electron look like?

While a treatment of electron spin can be found in any introductory textbook, I've noticed that the electron's magnetic field seems to be treated classically. Presumably this is because a quantum ...
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2answers
44 views

Why would classical correlation in Bell's experiment be a linear function of angle?

Sorry if it's a newbie question, but I have trouble understanding the following part in the Wikipedia's explanation for the Bell's theorem: With the measurements oriented at intermediate angles ...
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2answers
95 views

Could the universe have evolved WITHOUT the non-determinism of quantum mechanics? [on hold]

(I'm going to make a few conjectures here - please answer the question in light of them as if they were true, even though of course they may be overly simplistic or wrong) Assuming that: the ...
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2answers
96 views

Does Free Will Theorem imply that quantum mechanics plays crucial role in our brain’s functioning (consciousness)?

Is opposite statement of Free Will Theorem right: If elementary particles have a certain amount of free will, then so must we? Because to me elementary particles does have a bit of free will – quantum ...
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73 views

Bloch theorem, Energy, Free electron

I'm trying to learn on my own a bit of solid physics to tackle semiconductors afterwards. I'm struggling with the Energy versus $k$ diagrams for a free electron which shows that for a single value of ...
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1answer
51 views

Macroscopic Forces from QED

In QED the carrier for electromagnetic interaction is a photon, while macroscopic forces are due to electromagnetic interaction (by macroscopic forces I mean: normal force, object collision, friction ...
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Determine unknown potential & Hamiltonian in Schrödinger equation [on hold]

$x$ - time dependent Cartesian coordinate ; $m$ - time dependent mass of particle; Potential energy - unknown ! Hamiltonian - unknown ! Tasks: Make a formula to predict the $X(t$) ($x(t)$ for ...
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2answers
43 views

Can we correctly define momentum operator only by means of position operator and their commutation relation?

In "J.M. Ziman. Electrons and Phonons: The Theory of Transport Phenomena in Solids" the author formally introduces the position (displacement) operator and then defines the momentum operator with the ...
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1answer
36 views

Will an electron gun fire behind it?

If an electron travels as a wave, can it therefore not be aimed with any precision? If you fire an electron gun, can't you aim it at a particular slit? If the electron travels as a wave, will an ...
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0answers
39 views

Berry's phase: in which space does the degeneracy appear?

This question follows a previous one of mine: Adiabatic theorem and Berry phase. In his original paper [ M. V. Berry, Proc. R. Soc. Lond. A. Math. Phys. Sci. 392, 45 (1984) ], Berry discussed the ...
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0answers
26 views

What is it that makes an electron maintain a distance from the positively charged nucleus? [duplicate]

What is it that makes an electron maintain a distance from the positively charged nucleus? Why aren't electrons merely pulled into and absorbed by the nucleus ?
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2answers
74 views

What is the performance of a silicon crystal that makes it an essential component to computing

I'm on a thread of interest in the precise physics that allow the creation of the computing process. It began as a question posted in search of an understandable explanation of what physical form ...
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1answer
32 views

Quantum mechanical proof of Conway's SPIN and TWIN axioms?

I think I understand correlations of EPR-state and GHZ-state which deal with spin-1/2 particles and (-1, 1) measured values. Conway's state is spin-1 particle state with (-1, 0, 1) measured values. ...
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1answer
28 views

Beam splitters for X-rays?

What is the lower bound for the wavelength concerning polarizing beam splitters? Especially I ask for interferometer experiments with single photons. Of course I know that they exist for all ...
3
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1answer
96 views

Local number operators in quantum field theory

Redhead claims in his paper "More ado about nothing" (http://link.springer.com/article/10.1007%2FBF02054660) that number operators associated with different space points (at fixed time) fail to ...
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1answer
54 views

Does this photograph portray double muon impact with nanogold atoms?

1PHOTO 1: Macro-photograph of an NIH/FDA TEM of a nanogold dark stained biological sample projected onto Silver Halide (AgX) photographic gel paper. On June 10 I questioned if PHOTO 1 ...
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1answer
29 views

$m_l=0$ in Hydrogen atom of Scrodinger equation

$m_l=0$ corresponds to s-orbital and the values associated are: $$\lambda=2\pi r/m_l\to\infty$$ It means a wave of of infinite wavelength has a constant height at all values of $\phi$(azimuthal ...
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2answers
35 views

Superpositions and expectation values in quantum mechanics

When the wavefunction of a particle is not an eigenfunction of an operator, the property to which the operator corresponds does not have a definite value, Why? Also consider a linear combination of ...
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1answer
45 views

Observables in Quantum Mechanics

Studying on own quantum mechanics I came across: Preceeding text: A basic postulate of quantum mechanics tells us how to set up the operator corresponding to a given observable. Observables, ...
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2answers
63 views

Differences between wave function and set of orthonormal wave functions?

I'm reading a QM book. It first says for wave function: "The state of a physical system (or particle) is completely specified by an entity associated with it called a wave function, Ψ , that in ...
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1answer
33 views

Double-slit experiment and an experimental laboratory without photons

In order to see interference pattern of an electron, after the shot, an electron must not interact with any photon. So I'm asking how can such an photonless area can be created in the universe? And ...
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2answers
51 views

Does yukawa potential of two particles have effect on each other?

Okay,a novice here.Suppose two particle interact with Higgs field.Does The Yukawa potential created by each of them affect each other or the interaction in any way.If so,what is it physical ...
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2answers
96 views

About Quantum Mechanics

Did Feyman suggest even though Q.M. has great predictive power no one will ever really understand it ? Some people have said there may be hidden variables that explain underlying principles of Q.M. ...
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1answer
29 views

Equation for Photon and Electron Propagation [on hold]

What equation accurately describes the movement of a photon? Does this equation also apply to the movement of an electron?
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0answers
50 views

Quantum Boltzmann Equation

What is the Quantum Boltzmann equation and what does it describe? I think it describes the propagation of electrons and photons but I am not sure.
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1answer
65 views

Postulate of Quantum Mechanics on Wavefunction collapse [on hold]

There is a postulate in quantum mechanics about wavefunction collapse. Can anyone provide me some intuitive perspective into it along with the concept of projection (I mean mathematical treatment).
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2answers
29 views

Finding Interatomic Spacing

Here is the problem I am working on For what temperatures are the atoms in an ideal gas at pressure P quantum mechanical ? Hint: use the ideal gas law P V = N kT to deduce the interatomic spacing ...
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1answer
71 views
+50

Boundary Element Method or Boundary Integral Method Computational Aspects

I have to solve a Helmholtz equation inside a simply connected domain. I know that in general the boundary integral can be written as, $$\phi(x)=\int_V G(x,x') \rho(x')\ d^3x'+\int_S ...
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1answer
50 views

Finding particles in the classically forbidden regions [duplicate]

Have particles ever been found in the classically forbidden regions of potentials? For example, in a square well: has an experiment been able to find an electron outside the rectangular well (i.e. in ...
3
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0answers
38 views

Output of a beamsplitter with photon number (Fock) state inputs

Given a beamsplitter drawn below, where $\hat{a}$ and $\hat{b}$ are input modal annihilation operators, transmissivity is $\tau\in[0,1]$, and output modal annihilation operators are ...
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2answers
53 views

Phase space derivation of quantum harmonic oscillator partition function

I would like to derive the partition function for the quantum Harmonic oscillator from scratch: $$\tag{1} Z = \int dp \, dx\, e^{-\beta H}.$$ The free particle appears in many textbooks. $H = ...
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0answers
14 views

Quantum observation in the double slit experiment? [duplicate]

As far as quantum observation, when a human observes electrons going through the double whole experiment, have scientist tried having a blind person observe the experiment to see if the electrons ...
4
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3answers
90 views

Complex Dirac field in antiparticle description

I understand that the Dirac equation has negative and positive sets of solutions and this contributes to its quantization by a superposition of two Fourier modes represented as creation and ...
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0answers
12 views

Short clips with transcripts about interesting physical phenomena [closed]

I want to use of some interesting short clips with their transcripts at physics related to fundamental physics or quantum mechanics or physical phenomena. Can any user guide me?
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0answers
18 views

Detect missing frequencies in a frequency distribution

I have photons with a frequency distribution where one frequency is completly cut out. For example a frequency distribution like that: My question is: How precise can the position (frequency) of ...
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1answer
53 views

How to get the time derivative of an expectation value in quantum mechanics?

The textbook computes the time derivative of an expectation value as follows: $$\frac{d}{dt}\langle Q\rangle=\frac{d}{dt}\langle \Psi|\hat Q\Psi\rangle=\langle \frac{\partial\Psi}{\partial t}|\hat ...
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1answer
34 views

How does a system interact with environment in quantum mechanics? When would this interaction occur? What is it?

As title says, how does a system interact with environment? I realize that this interaction can lead to interference terms and non-diagonal terms in density matrix being reduced (quantum decoherence). ...
12
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5answers
2k views

Is the future already determined?

I've always wondered (and was re-inspired to explore further from these two videos) that if at a single point of time we know about the complete state (position, momentum, spins, everything.) of every ...
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1answer
41 views

Wave packets and amplitude

If a wave packet is given by: My question is basically how do we choose the write $A(k)$ to fit the particle we are looking at, or does it not matter (as my matter as my textbook seems to imply) ...
3
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1answer
77 views

What causes radioactivity? Is it a quantum mechanical effect?

I'm just curious what causes radioactivity. I've been told that in the case of alpha decay, since the nucleus is quantum mechanical, there is a probability that the configuration of protons and ...
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0answers
41 views

Can observables with discrete and continous eigenvalues be commuting?

In Dirac's The Principles of Quantum Mechanics he often uses the notion of "a complete set of commuting observables". This means a set of observables $\{\xi_1, \xi_2, \ldots, \xi_v, \xi_{v+1}, \ldots, ...
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35 views

Mathematical derivation of interference pattern for electrons?

One of the most famous experiments in quantum mechanics in the context of wave-particle duality is certainly passing a beam of electrons through two slits, which results in an interference pattern ...
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1answer
28 views

(Level: Undergrad) Continuity Conditions on the Wavefunction and Initial Values

I know that a physically meaningful $\Psi$ needs to be continuous. However, recently I came across a problem in which they were considering a wavefunction for the infinite square well potential and ...