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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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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$m_l=0$ 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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10 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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14 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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18 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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19 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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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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37 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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22 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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38 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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60 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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23 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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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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48 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 ...
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36 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
50 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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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 ...
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29 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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12 views

Short clips with transcripts about interesting physical phenomena [on hold]

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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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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49 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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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). ...
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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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40 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) ...
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72 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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37 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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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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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 ...
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If outside a cylindrical solenoid exist an electrical field what does that mean to the Aharonov-Bohm Effect?

To the question "What is the electric field outside a cylindrical solenoid when inside is turned on a magnetic field" the answer is that outside exists a electric field. Does that mean that the ...
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22 views

What is the most general definition of a bosonic Gaussian state?

I am reading this paper where the definition of the bosonic state is mentioned on page 2 here :- http://arxiv.org/pdf/0806.1625.pdf . From a general definition of any density operator in terms of ...
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3answers
63 views

Can stimulated emitted photons be absorbed?

Typically a stimulated photon will be one of a pair with its stimulating photon. If the leading photon is absorbed by a particle in the ground state, will it then be re-emited by the stimulated ...
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5answers
203 views

About the definition of expectation value in quantum mechanics

In quantum mechanics, the expectation value of a observable $A$ is defined as $$\int\Psi^*\hat A\Psi$$ But in probability theory the expectation is a property of a random variable, with respect to a ...
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60 views

Showing Dirac equation's Lorentz invariance and use of unitary matrix $U$

Dirac equation is $i \hbar \gamma^\mu \partial_\mu \psi - m c \psi = 0 $ To show its Lorentz invariance, we convert spacetime into $x'$ and $t'$ from $x$ and $t$ and then $( iU^\dagger \gamma^\mu ...
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92 views

Quantum states and state vectors

Does a state vector correspond to only one quantum states and the components in the state vector correspond to different states of this quantum state or is it that the components of the state vector ...
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85 views

What is the electric field outside a cylindrical solenoid?

What is the electric field outside a cylindrical solenoid when inside is turned on a magnetic field? The question is related to the question aharonov-bohm-effect-electricity-generation
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why does muon hop rate in metals change with temperature like this

you can find this figure in this pdf we use μSR to study the superconductor properties,,but I don't quite understand the T^-9 slope, does muon trapped in an interstitial site and hop rate drop with ...
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71 views

How to compute observables from the boson field operator?

I think I understand that if given the two boson wavefunction of two different states \begin{align} \Psi(\boldsymbol{r}_1,\boldsymbol{r}_2) = \dfrac{ \psi_1(\boldsymbol{r}_1)\psi_2(\boldsymbol{r}_2) + ...
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77 views

Why angular momentum about three independent axes?

The generic commutation relations for the angular momentum operator are $[J_x, J_y] = i \hbar J_z$, where the $J_i$, $i = x,y,z$ are the components of the angular momentum vector operator, $\mathbf ...
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38 views

Connection to spin 1/2 electron system?

In another Physics stack exchange thread here, Spin matrix for various spacetime fields I obtained the generator of rotations of the SO(2) rotation group for an infinitesimal rotation of 2D vectors. ...
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27 views

How to derive equation for probability current density in relativistic quantum mechanics [on hold]

How does one derive equation for probability current density in relativistic quantum mechanics? I am asking for textbook-styled explicit derivation. No need for any other background knowledge.
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1answer
66 views

Are operators in quantum mechanics linear transformations?

Observables in quantum mechanics correspond to self-adjoint linear operators. If $\psi$ is an eigenvector of $\hat A$, then $\hat A\psi=\alpha\psi$ where $\alpha$ is the eigenvalue of $\psi$. ...
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80 views

Expanding a ket in the position basis?

My textbook says that to find the ket $|ψ\rangle$ in the same position basis as the ket $|ø\rangle$ we do the following: $$|ψ\rangle=\int dø|ø\rangle \langle ø|ψ\rangle$$ Firstly can $|ø\rangle$ be ...
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Spontaneous breaking of a discrete non-Abelian symmetry

Can someone give an example of an one dimensional local gapped quantum lattice model with a discrete non-Abelian global internal symmetry that is spontaneously broken in the ground state? In ...
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Complete description of two electrons with spin

We have two electrons described by the wave function $\phi(\vec{x}_1,\vec{x}_2,s_1,s_2;t)$ where $\left| \phi(t)\right\rangle$ is the state vector and $(\vec{x}_1,\vec{x}_2,s_1,s_2)$ is the index of ...
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1answer
37 views

Fock matrix elements for RHF formalism

Here I refer to a particular book Molecular Quantum Mechanics by Peter W. Atkins and Ronald S. Friedman, but similar derivation could be found in many other texts. So, when obtaining the explicit ...
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43 views

Do randomness and indeterminacy in Quantum Physics mean the same?

I have been trying to learn about the randomness in Quantum Physics. But of the many sources I referred to, some say about "Randomness in Quantum physics" and some others say about "Quantum ...
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1answer
69 views

The Eigenstate Existence Problem in Dirac's 'Principles of Quantum Mechanics'

In Chapter II of Dirac's Principles of Quantum Mechanics, Dirac explains that in general it is very difficult to know whether, for a given real linear operator, that any eigenvalues/eigenvectors exist ...
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2answers
103 views

What is the analogy of $|x\rangle$ in quantum field theory?

Let me start from path integral formulation in quantum mechanics and quantum field theory. In QM, we have $$ U(x_b,x_a;T) = \langle x_b | U(T) |x_a \rangle= \int \mathcal{D}q e^{iS} \tag{1} $$ ...
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2answers
96 views

Aharonov-Bohm Effect electricity generation

This question is based on highly intuitive picture of the Aharonov-Bohm effect (perhaps a naive one). From what I have read, the current explanation of the AB effect is that although the electron ...
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1answer
33 views

Solving particle on a ring problem using momentum eigenvalue equation instead of energy eigenvalue equation

I have read somewhere that for particle on a ring problem you don't have to solve eigenvalue equation $H\psi=E\psi$ you can instead solve eigenvalue equation $P\psi=p\psi$ where P is momentum ...