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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25 views

Books on waves with Fourier Transforms

There are many waves and oscillations books out there that also include Fourier analysis but very few give the subject a thorough treatment, they just pass it in a few pages. If anybody has any ...
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6answers
472 views

Fermion vs. Bosons and particle vs. wave: is there a link?

I'm puzzled since several years on this basic aspect of quantum mechanics. Quantum theory is supposed to describe particle-wave symmetry of our world. It also describes our universe in term of bosons ...
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2answers
189 views

Is entropy a meaningful concept on a quantum level?

My naive assumptions, as I really am at a pretty basic stage in QM, are as follows: Classically, entropy gives us a practical measure of the direction of time, as opposed to our physical laws which, ...
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0answers
39 views

What's the physical meaning of the different entanglement entropy of mixed bipartite systems?

As we know, for pure bipartite systems, the entanglement entropy are the same for both subsystems. But this is not the case for mixed states. Can anyone explain what's the physical meaning of this ...
2
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1answer
33 views

Sources to learn about Berry phases and Adiabatic Theorem

I recently went through Griffiths' Quantum Mechanics text and there is a chapter called the Adiabatic Theorem that includes Berry phase and the Aharonov-Bohm effect. As I found them very ...
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1answer
129 views

Quantum fluctuation

According to the quantum fluctuation concept, a particle and its corresponding antiparticle appear out of nothing only to annihilate and emit some energy in the form of electromagnetic waves. Does ...
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27 views

How to form a density matrix? [on hold]

forming a density matrix when two independent states are there
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0answers
42 views

Can a density matrix be complex? [on hold]

Normally a density matrix is thought of as a statistical ensemble of pure states. However, after using the Time-Evolution Equation (or Master Equation) to evolve a density matrix, they start to have ...
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0answers
28 views

Lippmann-Schwinger equation and $T$ expansion

Lippmann-Schwinger equation, in operator form, is: $$ T=V+V\frac{1} {E-H_0+i \hbar \varepsilon} T=:V+V\Theta_0T, $$ where $H_{tot}=H_0+{V}$ is the hamiltonian ($H_0$ is the free particle hamiltonian ...
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0answers
16 views

Can there be a link between non-locality and non-Markovianity?

Non-locality is a curious feature that is linked to the violation of Bell inequality of any form. It arise from the impossibility of simultaneous joint measurements of observables. The ...
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1answer
256 views

Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...
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1answer
34 views

Problem with tracing over the environment and obtaining reduced density operator

I'm reading an article by Bas Henson given here. On page 25 he deals with the double slit experiment Given the wavefunction which is his equation 1.75, he claims he has traced over the environment ...
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2answers
77 views

Why is local realism not possible with QM?

In Mermin's thought experiment (pdf) particles are sent to two detectors A and B with 3 settings each. If the particle passes the test, we get a green (G) light, else red (R). Now in QM we could send ...
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1answer
42 views

Barycenter and relative coordinates for schroedinger equation of the hydrogen atom

Heyho, i just realized i am not sure how one gets from: $\Big(-\frac{\hbar^2}{2m_e} \Delta_{r_e} - \frac{\hbar^2}{2M_P} \Delta_{r_p} +V(r) \Big)\Psi(r_e,r_p) = E \Psi(r_e,r_p)$ to: ...
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3answers
87 views

Is there free will? [on hold]

From what I've understood about the answer to this question quantum physics doesn't contradict determinism, but instead it simply isn't achievable only because of our universe's nature: we are unable ...
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3answers
358 views

Bound states of the $V(x)=\pm \delta'^{(n)}(x)$ potential?

The $\delta(x)$ Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives $\delta', \delta'', ...$ exist also, do they? If yes, can we look for ...
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0answers
68 views

Is there a proof that the number of eigenstates is countable for a bound system?

When you solve Schrödinger equation for a free particle with no boundary conditions your eigen states are indexed by quantum number $k \in \mathbb R $ and $\mathbb R$ isn't countable but if you add a ...
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1answer
13 views

magnet repulsion in a cylinder [on hold]

Firstly, Am doing a research project on the use of repulsion of magnets to form a car shock absorbers. Can the forces of repulsion manage to absorb the shock of a 2.0 ton car?
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31 views

Show that the minimum energy value for a given $l$ increases as $l$ increases

"Consider a particle in a central field and assume that the system has a discrete spectrum. Each orbital quantum number $l$ has a minimum energy value. Show that this minimum value increases as $l$ ...
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1answer
30 views

Fourier expansion and transform - what about the phase of the waves that i am adding?

Say we have a wave on the surface of the water and we want to describe it as a sum of other waves. So we use Fourier expansion to add waves of different wavelengths. For simplicity, say we have to ...
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3answers
64 views

Is there an example of a situation where you need a continuous spectrum?

If you had a hydrogen atom you could say that you want to be able to ionize them. But if you then add the potential due to the earth, e.g. ...
13
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1answer
484 views

How to evaluate this sum of coupling coefficients?

I would like to evaluate the following summation of Clebsch-Gordan and Wigner 6-j symbols in closed form: $$\sum_{l,m} C_{l_2,m_2,l_1,m_1}^{l,m} C_{\lambda_2,\mu_2,\lambda_1,\mu_1}^{l,m} \left\{ ...
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0answers
9 views

Can QKD nodes use a constantly evolving key?

In QKD we know that we can generate random secret keys using quantum entangled photons, measuring their qubits and then using noise reduction to negotiate probably similar bits between Alice and Bob. ...
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1answer
76 views

Is there any $SU(\infty)$ gauge theory in quantum field theory?

The groups $U(N)$ and $SU(N)$ are the most important Lie groups in quantum field theory. The most popular are the $U(1),SU(2),SU(3)$ groups (these gauge groups form the Standard model). But is there ...
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0answers
69 views

Bell's inequality, “complete plans” and spooky action at a distance

What am I proposing and asking? In Mermin's thought experiment entangled particles, i.e. photons are sent to two machines A and B with 3 settings each. The idea of a "complete plan" how to react to ...
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0answers
50 views

Can you have more than two entangled particles? [duplicate]

Given the diagram on the wikipedia page for Quantum Entanglement we a beam of photons hitting a crystal which splits the beam into to entangled particles. Is it possible to split the beam into four ...
2
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1answer
119 views

What is Z3 exciton?

I am searching and studying excitons and I confronted with a term named Z3 exciton. What is it? And what is its difference with, for instance Z1 or Z2 exciton?
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0answers
59 views

Decay of excited electron from Schrödinger equation?

I'm currently studying for a quantum mechanics exam. I found some old exams which has the following question I'm trying to solve. Please tell me if my reasoning is wrong. Can you see from the ...
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1answer
58 views

How to model matter in code [on hold]

I've always had a passion for science, understanding and programming. Given my interests, I thought a cool thing to do would be to model real world theories in code (with visuals) so that others may ...
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1answer
51 views

Can one detect a single photon through measuring its impulse/momentum on a mirror?

Can one detect a single photon through measuring its impulse/momentum on a mirror? If the answer if YES or theoretically possible, photon path and interference fringes can be detected simultaneously ...
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1answer
64 views

Can an electron go along different paths at once in a circuit

A single electron moves along a circuit and comes to a fork in the wires. The wires separate but come back together near the end of the circuit. From what I know, the electron will travel along all ...
6
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2answers
94 views

Infinite square well that suddenly decreases in size

A well known exercise in basic quantum mechanics is the sudden (diabatic) increase of the length of an infinite square well. Now consider a particle in an eigenstate of an infinite well that is ...
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1answer
59 views

Children of entangled particles

Theres a photo on the wikipedia page Quantum Entanglement there's a image of a photon being split into two entangled photons via crystal. I used this picture to demonstrate the scenario below. ...
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Are the produced entangled photons in type II SPDC always in phase?

Are the produced entangled photons in type II SPDC (spontaneous parametric down conversion) always in phase? In Kim's delayed choice quantum eraser, two entangled photons are produced by a BBQ ...
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0answers
64 views

Symmetry in quantum mechanics

I originally asked this on the maths site, but I'll repost it here. Let $\mathcal{H}$ be the separable Hilbert space associated to some quantum system, and let $\langle\cdot,\cdot\rangle ...
4
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1answer
77 views

Does a Buckyball spin like an electron or like a baseball?

Does a Buckyball spin like an electron or like a baseball? We are often told that an electron does not really spin like a baseball. Only one (or two, if you count up and down) spin states, for ...
3
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1answer
117 views

Path dependent phase in quantum mechanics

In elementary treatments of quantum mechanics, we are taught that the wavefunction of a single particle is complex valued ($\Psi : \mathbb{R}^3 \to \mathbb{C}$). In particular, the wavefunction has a ...
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2answers
157 views

Quantum entanglement and special relativity PARADOX [on hold]

Imagine two entangled atomic clocks. After we entangle them, we measure the time: it does has to be the same , right ? Now lets suppose that we entangle them , but don't measure them, then we plant ...
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1answer
60 views

is there an operator which measures the mass of particles?

When I studied a spin, the textbook said spin is an intrinsic quantity like mass. However, while we can calculate just expectation values $ \langle \textrm{S}^2\rangle $ or $ \langle S_z\rangle $, the ...
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2answers
67 views

Natural Philosophy [on hold]

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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1answer
142 views

Slit width for minimum spot size in electron slit diffraction if involving uncertainity principle

I don't believe the following is an accurate description of the physical but a homework problem to help understanding. A beam of electron of energy 0.025 eV moving along x-direction, passes ...
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1answer
27 views

How to produce a given entangled state of two quantum bits?

I was watching Leonard Susskind's video series on quantum entanglement, where he looks at the spins of two electrons. In particular, there are entangled states of the form $$\alpha\left|\uparrow ...
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2answers
61 views

Does Quantum Collapse occur?

Collapses, Quantum Jumps, and the Born interpretation. In my mind they are all the same. But some serious physicists (Schlosshauer, for example) claim there is no evidence for the existence of ...
2
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1answer
65 views

Fourier Transforms of position and momentum space in Quantum Mechanics

Fourier transformations: for momentum space and for position space. How do we know that Ψ is not the Fourier transform of Φ but we suppose that its the other way around(Ψ would be ...
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1answer
57 views

How to deal with eigenvectors which are not square integrable?

In Quantum Mechanics there is one type of situation I'm still unsure on how to deal with. First of all, I want to make clear I'm trying to understand how to deal with this rigorously. What I'm talking ...
11
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2answers
541 views

Are Thomas Breuer's subjective decoherence and Scott Aaronson's freebits with Knightian freedom the same things in essence?

In his remarkable works (1,2 and their recent development 3) Thomas Breuer proves by diagonalization the phenomenon that the observer cannot distinguish all phase space states of a system where he is ...
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2answers
1k views

Is the movement of electrons truly random?

The result of rolling dice is considered pseudo-random because it depends on an almost endless list of factors (how you roll it, the terrain it lands on, etc.), but it is not TRULY random. Is the ...
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2answers
35 views

Quantum entanglement thought experiment

One can "filter" a collection of electron pairs generated in an entangled (fixed-direction) spin state (e.g. singlet $\left|\uparrow \downarrow \right\rangle - \left|\downarrow \uparrow\right\rangle$) ...
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1answer
31 views

Expected value of an operator in the microcanonical ensemble

I am following professor David Tong's lecture notes on Statistical Mechanics and on page 9 of this file http://www.damtp.cam.ac.uk/user/tong/statphys/one.pdf he states that the expected value of an ...