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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Superposition of waves with different initial phase in Quantum Mechanics [closed]

In Quantum Mechanics, if a particle's state is a superposition of many states, then we say that its position is well-defined (by the Heisenberg uncertainty principle, because here we have ill-defined ...
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1answer
406 views

Does time reversal symmetry hold for (kitaev model) 1D spinless $p-$ wave superconductor?

The hamiltonian 1D spinlesss p wave superconductor can be written as $$ H=\sum_k \phi_k^\dagger \begin{pmatrix} \xi(k) & 2i\Delta \sin(k)\\ -2i\Delta \sin(k ) & -\xi(k)\end{pmatrix}\phi_k $$ ...
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2answers
155 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
674 views

Probability current density : Isn't there something wrong with this proof?

Is there something wrong with the following proof (see below)? To me, it seems like the third line should show $$\frac{dP_{ab}}{dt}=-\int_a^b \frac{\partial}{\partial t}J(x,t)dx$$ Am I missing ...
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68 views

What is the group transformation property of photons under rotation?

Both the photon and the W boson are spin-1 particles. Under rotation W boson must transform under the 3-dimensional representation of SU(2). However, the photon has two degrees of freedom (or helicity ...
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167 views

At what point does everything become nothing?

I understand that the universe, which I'll call "everything", is expanding and it used to be much smaller. But I keep hearing assertions about a universe coming from nothing. If you rolled the clock ...
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1answer
120 views

How many eigenstates for four (non-identical) spin 1/2 particles? [closed]

Question Consider a system of four non-identical spin 1/2 particles. Find the possible values for the total spin and state the number of eigenstates for each of these. Attempt So I coupled S1 and ...
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0answers
355 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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102 views

How does commutation between the hamiltonian and angular momentum operator (squared) imply conservation of Angular momentum?

So we are looking at central potentials in QM; The lecturer poses the question, when is $\textbf{L}$ conserved? He then considers the commutator of $\hat{H}$ and $\hat{L^2}$. We have; $$\hat{H}=-\...
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2answers
72 views

What is the correct way to treat operators that has “time” in QM? [duplicate]

I don't know if this question has already been resolved but considering that $i\hbar\partial_t$ is the energy operator, and $\partial^2_t$ is the waves operator (or helmholtz), I can't accept that $t$ ...
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92 views

Current quantum theory of interference

I have always thought that the quantum theory states that interference occurs when photons behave like waves and two or more possible paths exist. Interference can then be destroyed if the path of the ...
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3answers
89 views

Decrease of uncertainty of momentum with increase of width of infinite well in QM(intuition)

Why does the uncertainty in the momentum decrease with the increase of the width for an energy eigenstate in the classic problem if the infinite well in Quantum Mechanics? I have worked out the ...
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1answer
187 views

Experiment that demonstrates the wave-particle duality of electrons

EDIT : You're about to read the first iteration of my question which is flawed. Please go to the end to see an illustration of what I meant to say. The phenomenon I was talking about is called ...
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2answers
604 views

The uncertainty principle and spin

I realize that this may be a very basic question, but I've been unable to find the answer elsewhere so thanks in advance for the help. Suppose an electron's spin is measured about an axis, and then ...
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2answers
133 views

multiverse fabric of reality

Source-"fabric of reality"- author d. deutsch - his contention, as I understand it, is that quantum interference is caused by "almost, but not identical quite quantum entities" , e.g. electrons, from ...
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138 views

In Quantum mechanics, what is realism? [closed]

Some interpretations of QM are realist and some are anti-realist. But, it is the idea that something exists before it is measured, correct?
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231 views

Direct nuclear reactions problems [closed]

can anyone explain Multi-step nuclear reactions in terms of direct nuclear reactions .
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2answers
220 views

Linearity in Quantum Mechanics that make superposition possible

As a beginner in QM, all the video lectures that i have seen talk about superposing wave functions in order to get $\psi$. But from what i know from linear algebra, the system must be linear in order ...
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2answers
227 views

Show that the energy levels of a particle in a specific potential are $E_n=(n+\frac{1}{2})h\omega-\frac{1}{2}\frac{F^2}{m\omega^2}$ [closed]

A particle of mass m moves on the x-axis under the influence of the potential $$V(x)=\frac{1}{2}m\omega^2x^2+Fx$$ Can anyone help me, using Schrödinger's equation in one dimension that the energy ...
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3answers
258 views

How “things” radiate electromagnetic radiation? [closed]

How things radiate electromagnetic radiation? I don't ask why they radiate (higher temperature than 0K) but how they radiate this electromagnetic waves?
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2answers
106 views

Natural Philosophy [closed]

My question is an extension of the celebrated question on the moon’s existence if unobserved. “do we still have tides on earth if the moon is unobserved?”
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5answers
279 views

Which symmetric pure qudit states can be reached within local operations?

There are two pure symmetric states $|\psi\rangle$ and $|\phi\rangle$ of $n$ qudits. Is there any known set of invariants $\{I_i:i\in\{1,\ldots,k\}\}$ which is equal for both states iff $|\phi\rangle=...
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4answers
621 views

Is the quantization of the harmonic oscillator unique?

To put it a little better: Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit? I'm specifically, but not only, interested in an ...
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5answers
847 views

Is double-slit experiment dependent on rate at which electrons are fired at slit?

I am a mathematician and I am studying string theory. For this purpose I studied quantum theory. After reading Feynman's book in which he described the double-slit experiment (Young's experiment) I ...
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3answers
439 views

How axiomatic is the symmetrization requirement (i.e. the Pauli principle)? (in QM)

I've so far always been told, that the symmetrization requirement is an axiom on the level of the Schrödinger equation and the statistical interpretation of the wave function (or it's absolute value). ...
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What does imaginary number maps to physically?

I am taking undergraduate quantum mechanics currently, and the concept of an imaginary number had always troubled me. I always feel that complex numbers are more of a mathematical convenience, but ...
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2answers
1k views

Conjugate Variables, Noether's Theorem and QM

What is the underlying reason that the same pairs of conjugate variables (e.g. energy & time, momentum & position) are related in Noether's theorem (e.g. time symmetry implies energy ...
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2answers
1k views

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 ...
7
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2answers
108 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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2answers
2k views

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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3answers
5k views

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 ...
7
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3answers
1k views

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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6answers
552 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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6answers
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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 ...
6
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2answers
338 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 ...
6
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1answer
141 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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3answers
494 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 ...
6
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1answer
428 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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2answers
422 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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2answers
584 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 ...
5
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1answer
261 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
68 views

Which charge to use in the Dirac quantization condition?

I have a follow-up question to Dirac magnetic monopoles and quark fractional electric charge quantization, regarding whether the "unit of electric charge" in the Dirac quantization condition should be ...
5
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2answers
402 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)}{\...
5
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2answers
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 ...
5
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3answers
601 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,...
5
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2answers
165 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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644 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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2answers
3k views

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 \...
5
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1answer
796 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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2answers
273 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 ...