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 quantum-field-...

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Is a single photon always circularly polarized?

While trying to understand polarization in quantum field theory, I wondered how a single photon could go through a linear polarizer. I found a paper which asked "Is a single photon always circularly ...
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Slowing down light in an opaque crystal for a whole minute

I just read about a team of physicists at the University of Darmstadt, Germany, that managed to completely slow down a beam of light that traveled through an opaque crystal (article here). How is it ...
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How is temperature related to color?

I spent some time studying about temperatures and color of objects. It turns out that as we heat something it turns to red, then yellowish white and if we heat it more it turns to bluish-white. Like ...
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Is the expectation value always an eigenvalue?

Must the expectation value of an observable always be equal to an eigenvalue of the corresponding operator? I already know that 0 is not an eigenvalue, but are there any other examples?
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105 views

How can quantum tunnelling lead to spontaneous decay?

I have never understood what measuring process (if any) is supposed to be continuously polling the quantum state of an unstable bound system subjected to decay via quantum tunnelling. The reason I ...
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535 views

Can quantum entanglement be simulated on a digital computer to any degree of precision?

First principles modelling of physical phenomena has been very successful in physics. The largest limitation is perhaps the fact that many QM problems are NP hard so we would need really powerful ...
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483 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
417 views

Why do we must initially assume that the wavefunction is complex?

The sound waves are real, and they can interfere, so corresponding apparat may be used in quantum mechanics. We also may use the time dependence in a form of orthogonal matrix multiplying the initial ...
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704 views

Why is the Dirac equation not used for calculations?

From what I understand the Dirac equation is supposed to be an improvement on the Schrödinger equation in that it is consistent with relativity theory. Yet all methods I have encountered for doing ...
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337 views

Mathematical probabilistic interepretation of probability amplitude

As a warning, I come from an "applied math" background with next to no knowledge of physics. That said, here's my question: I'm looking at the possibility of using probability amplitude functions to ...
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1answer
138 views

Are composite bosons always bosonic (e.g. the pion-cloud surrounding the nuclei)?

The $\pi$-meson is a boson, but consists of quark-antiquark (fermions). It seems to me that at some energy level (equivalently distance) the inner structure (fermionic nature of the quarks) of the ...
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422 views

Can a photon exhibit multiple frequencies?

Can a photon be a superposition of multiple frequency states? Kind of similar to how an electron can be a superposition of multiple spin states.
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What happens when a photon hits a beamsplitter?

Yesterday I read that we can affect the path and the 'form' (particle or wave) of a photon after the fact (Wheeler's delayed choice experiment). Part of what is puzzling me is the beam-splitter. Are ...
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576 views

Some doubts about photons

I am reading Berkeley Physics Course vol. 4 (Quantum Mechanics) , chapter 4 (photons). (1) Section 46: book says: consider a typical photon emitted by the source. It can be regarded as a a wave ...
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397 views

Time-dependent Schrödinger equation with $V=V(x,t)$

I was wondering about the following: If you have the time-dependent Schrödinger equation such that $$i \hbar \frac{\partial\psi(x,t)}{\partial t} = - \frac{\hbar^2}{2m} \frac{\partial^2\psi(x,t)}{\...
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2k views

Canonical momentum in different coordinate system

The canonical momentum is defined as $p_{i} = \frac {\partial L}{\partial \dot{q_{i}}} $, where $L$ is the Lagrangian. So actually how does $p_{i}$ transform in one coordinate system $\textbf{q}$ to ...
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114 views

Free Will Theorem question

The Kochen-Specker Theorem says, if I understand it correctly, that the results of spin measurements cannot be predetermined independent of measurement. They get to this conclusion by describing 33 ...
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3answers
290 views

Why do Bell tests give perfect correlations?

Suppose some decay process emits 2 electrons in opposite directions, and their spin is measured by a Stern-Gerlach type device in a particular direction, say Sz. The books say that if 2 detectors have ...
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1answer
257 views

Why do electrons not bump into impurities in a superconductor?

Just a simple question. Why is it, that when a material becomes superconducting, and by that gets zero resistivity, the electrons don't hit impurities in the material? For the material to have zero ...
5
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1answer
784 views

Feynman's 'diamond jumping out of a box' parody, how would this work?

I have been told that Feynman deduced from a path integral formulation an equation that predicts the amount of time it would take for a diamond to 'jump' out of a box: $t > \dfrac{x \Delta{x} m}{ ...
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4answers
2k views

Annihilation and Creation operators not hermitian

The annihilation and creation operators are given below $$ \hat a|n\rangle=\sqrt{n}|n-1\rangle\qquad\text{and}\qquad\hat a^\dagger|n\rangle=\sqrt{n+1}|n+1\rangle $$ Now I know the operator a^ is not ...
5
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2answers
270 views

Proof of conservation of information [duplicate]

After listening of some lectures of Leonard Susskind about black holes, he mentioned that conservation of information is one of the foundations of physics. After searching the web I cannot seem to ...
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3answers
595 views

Confusion about wavefunction separability

A wavefunction is inherently a multi-particle function. If you have a container that is perfectly isolated from the external universe (not possible, but just imagine it) and filled with $n$ particles,...
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1answer
678 views

Do mutual eigenkets imply commutation of two operators?

I have been working on this question. I have solved it, and I would like to check whether my line of reasoning is right or wrong Question: Prove that if there exists a mutual complete set of ...
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164 views

Do asymptotically similar potentials yield similar energy levels asymptotically?

Let there be given two Hamiltonians $$H_1~=~ p^{2}+f(x) \qquad \mathrm{and} \qquad H_2~=~ p^{2}+g(x). $$ Let's suppose that for big big $x$, the potentials are asymptotically similar in the sense ...
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638 views

Rationale for writing wave function as product of independent wave functions

When solving Schrödinger's equation for a 3D quantum well with infinite barriers, my reference states that: $$\psi(x,y,z) = \psi(x)\psi(y)\psi(z) \quad\text{when}\quad V(x,y,z) = V(x) + V(y) + V(z) = ...
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Pauli matrix rotations

When doing physics with two-level systems and introducing rotations, a term that appears quite often is the rotation of a Pauli matrix by another one: $$e^{- i \sigma_j \theta/2} \sigma_k e^{i \...
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2answers
757 views

Shor's algorithm and Bohmian Mechanics

Do quantum computer's tell us anything about the foundations of quantum theory? In particular Shor argued in the famous thread by 't Hooft Why do people categorically dismiss some simple quantum ...
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1answer
132 views

Orbital angular momentum of electrons

In a QM class, to study the hydrogen atom, we started by defining the Hamiltonian $H$ for a central potential, then made an orbital angular momentum operator appear as part of $H$, then down the line ...
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2answers
819 views

Again about all-win lottery

I suggest the following thought experiment that describes a machine which makes everybody happy. Suppose a lottery is conducted. The winner is awarded a billion dollars plus the title of eternal ...
4
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1answer
427 views

Classical (or semi-classical) interpretation of photoelectric effect?

This site says that "it has recently been proven that the photoelectric effect can be interpreted classically (or at least semi-classically) in non-particle, wavelike terms". Is anyone familiar with ...
4
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2answers
207 views

How to use the Born rule to find the expected outcome of this simple Stern-Gerlach experiment [closed]

The experiment is shown below. How do I calculate the probability of observing a count in detector A, B, or C? Sakurai's text for example starts out describing how to calculate the outcome of simpler ...
4
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1answer
250 views

Is this a photograph of an electron-positron annihilation? [closed]

With degrees in Mechanical and Electrical engineering but no advanced education in physics, I submit a query based on ellipsometric macro photography of TEMS supplied by FDA/NIH. In one TEM a ...
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Momentum eigenstate definition in Eq (2.5.5) of Weinberg Vol. 1 clairification

This is question is related to one asked here: Questions concerning some parts of the section on one-particle states in Weinberg's first volume on QFT. In Eq (2.5.5) of Weinberg's "The Quantum ...
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3answers
886 views

Historical background of wave function collapse

I wonder what were the main experiments that led people to develop the concept of wave function collapse? (I think I am correct in including the Born Rule within the general umbrella of the collapse ...
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2answers
247 views

How to derive the Aharonov-Bohm effect result?

In the derivations of the Aharonov-Bohm phase, it is directly mentioned that due to the introduction of the vector potential $A$, an extra phase is introduced into the wavefunction for case $A\neq0$ i....
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568 views

Has BCS Cooper pair condensate been observed in experiment?

Feshbach resonance in s-wave scattering states a BCS Cooper pair condensation at B-field just above the resonance where the scattering length a <0. Just wondering if the condensation has been ...
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2answers
170 views

Does $\sigma_x\sigma_p = 0 \cdot \infty$ after a measurement of particle position?

I feel this question has an obvious answer that I should have been able to find independently, but I've searched for a while now it hasn't clicked. When position is measured, the uncertainty of the ...
4
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1answer
208 views

Does electromagnetic field collapse the wave function of charged particles?

In an electron double slit experiment, let's put two charged plates behind the slits in an attempt to move the pattern up and down on the the screen. What will happen? Will it just shift the ...
4
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2answers
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Quantum momentum (De Broglie)

The de broglie hypothesis suggests a particle can be associated with a wave of momentum $p = \hbar k$ my question is the following: how does one arrive at this concept of the momentum of a wave? I ...
4
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1answer
669 views

Questions about angular momentum and 3-dimensional(3D) space?

Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
4
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1answer
344 views

Off-diagonal elements of Hamiltonian matrix $H_{12}$ & $H_{21}$: energy of transition from $|1\rangle$ to $|2\rangle$ or amplitude of transition?

$$ \newcommand{\k}[1]{\left| #1 \right\rangle} \newcommand{\dd}[1]{\frac{d #1}{dt}} $$ In a Hamiltonian Matrix like this: $$H = \begin{pmatrix} E_{11} & E_{12} \\ E_{21} & E_{22} \end{...
4
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1answer
605 views

Confused by Many-Body Formalism: Creation/Annihilation to Field Operators

I'm going through an introduction to many-body theory and I am getting tripped up on the formalism. I understand quantities such as $\hat {N} = \sum_{i}\hat{n}_{i}=\sum_{i}\hat{a}_{i}^{\dagger}\hat{a}...
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1answer
353 views

How does Cooper pairing work?

Cooper pairs are one of the models how superconductivity is explained. What still baffles me is how a vibration of the crystal lattice (the so-called phonon) can interact with the electron (an actual ...
4
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1answer
234 views

Eigenvalue of $L_z$

In section 4.3 of Griffths' "Introduction to Quantum Mechanics", just below Figure 4.6, the sentence begins Let $\hbar \ell$ be the eigenvalue of $L_z$ at this top rung... Why is this valid? ...
4
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1answer
211 views

Products of Gaussian stochastic process variables

In the classic experimental physics text "Statistical Theory of Signal Detection" by Carl. W. Helstrom, Chapter II, section 4 concerns Gaussian Stochastic Processes. Such a process is observed at ...
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1answer
215 views

Understanding the Particle Data Group review documents

Would someone mind outlining what each piece of semi-structured data means in these images taken of some PDG documents? As a newcomer it is very difficult to interpret the tables. tl;dr This ...
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2answers
964 views

Use of Operators in Quantum Mechanics

I understand the form of operators in use for quantum mechanics such as the momentum operator: $$\hat{\text{P}}=-ih\frac{d}{dx}$$ My question is in what ways can I use it and what am I getting back? ...
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512 views

Extending the idea of superdense coding

I was reading through the superdense coding protocol, that lets A convey two classical bits to B by sending one qubit (assuming B sends A a qubit beforehand). So B creates a 2-qubit state and sends ...
4
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1answer
417 views

Is momentum still conserved in non-phase-matched nonlinear optical processes?

To be efficient, a phase-matching condition has to be fulfilled in many nonlinear optical processes. For instance, the phase-matching requirement for second-harmonic generation is $k_{2\omega}=2k_{\...