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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200 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 ...
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1answer
68 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
77 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 ...
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2answers
53 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
60 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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1answer
109 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 ...
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2answers
360 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
119 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 ...
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1answer
58 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
388 views

Fourier Transforms of position and momentum space in Quantum Mechanics

Fourier transformations: $$\phi(\vec{k}) = \left( \frac{1}{\sqrt{2 \pi}} \right)^3 \int_{r\text{ space}} \psi(\vec{r}) e^{-i \mathbf{k} \cdot \mathbf{r}} d^3r$$ for momentum space and ...
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1answer
346 views

Commutation between Dirac hamiltonian and angular momentum

In reading about angular momentum and spin, I came across a derivation showing that the Dirac Hamiltonian does not commute with orbital angular momentum, and hence L is not conserved. What is it about ...
2
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1answer
82 views

Can someone explain why this QM FTL communication setup is wrong?

So I thought I understood the double-slit experiment and EPR paradox until this setup occured to me. It combines EPR entanglement with "which-way" double slit setups. I know it must be wrong, but I ...
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1answer
159 views

Trivial representation in Clebsch-Gordan decomposition

My professor defined the Clebsch-Gordan series as the direct sum decomposition of the tensor product of two representations of the Lie group SU(2): $$ D_{j_1} \otimes D_{j_2} = D_{j_1+j_2} \oplus ...
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1answer
82 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
88 views

Can we reconstruct 1D potentials in QM from the spectrum? [duplicate]

Knowing the potential, we can find the spectrum of the Schrödinger operator. The converse question is: Knowing the spectrum, can we reconstruct the potential? As an example, a harmonic potential has ...
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2answers
48 views

Is there a version of “delayed choice” for sound waves?

I'm familiar with the uncertainty principle in harmonic analysis, which states that you can't localize the support of a function in both the time domain and the Fourier domain. One of the physical ...
3
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1answer
214 views

Planck's constant and phase space in quantum mechanics

During my undergrad physics classes, I've come across several seemingly related phenomena dealing with $h$ and phase space in quantum mechanics. Let $T_x$ be a translation operator by $x$ in ...
2
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1answer
91 views

How to understand the three state descriptions from 3 observers of such a system?

Assuming an EPR pair $\psi_{AB}=|00>+|11>$ and three observers Alice, Bob and Charlie, who can communicate with each other but they do not do it for the time being. Alice with a qubit $|0>$ ...
2
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2answers
106 views

Spin-orbit model; Hamiltonian seems to be non-Hermitian

I'm working on an exercise and I'm getting quite stuck. We define $\sigma$ as the vector of Pauli matrices.The Hamiltonian is formulated as: $ H_1 = -\frac{\hbar^2 k^2}{2 m} + \alpha \left(\sigma ...
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1answer
73 views

Fractional number of particles in the universe?

Is it possible, that the metagalaxy contains a fractional (non whole) number of particles or fractional number of a particular kind of particles (such as electrons)? Sorry, if my question is stupid, ...
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2answers
68 views

Pair Production in Entangled Photons

Two high-energy photons are entangled and go their separate ways. One of them undergoes pair production by interacting with an atomic nucleus, and this is observed. Does the other photon also undergo ...
2
votes
1answer
715 views

Controlled Phase Gates

The Quantum Fourier Transform consists of 2 gates. Controlled Phase Gates, and Hadamard gates. I'm assuming the Controlled Phase Gate is a combination of a Control Gate, and a Phase Gate. But what ...
2
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1answer
67 views

finding generic Quantum circuits for k-local hamiltonians

Let $P_n$ denote the Pauli group on $n$ qubits (think of n as a large number). Let $G=\left<g_1,...,g_n\right> < P_n$ be some abelian subgroup such that each $g_i$ acts on at most $k\ll n$ ...
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2answers
84 views

Using slope=0 technique to find most likely spherical shell

In this PDF http://riedo.gatech.edu/Teaching/Modern_Physics/hw/HW3_2010_MP_SOL.pdf problem#1, the instructor solves the question of which spherical shell (what radius $r$) has the greatest ...
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3answers
336 views

How to understand the motion of a particle in Quantum Mechanics?

In Classical Mechanics when we talk about the motion of a particle it is the same as talking about the idea of trajectory. The fact is that in Classical Mechanics, a particle has a definite position ...
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1answer
60 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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2answers
555 views

Schroedinger equation for hydrogen atom

I have got a problem understanding the meaning of the Laplace operator in the Schrödinger equation for the hydrogen atom. $$\Big(-\frac{\hbar^2}{2m_e} \Delta_{r_e} - \frac{\hbar^2}{2M_P} \Delta_{r_p} ...
2
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1answer
152 views

Quantum Liouville-Propagator Operator Trace Identity [closed]

How can i proove: $Tr(Ae^{Lt}B)=Tr(Be^{-Lt}A)$ were $A$ and $B$ are Observables in the Schrödinger picture and $L$ is the Quantum Liouville super-operator defined by: $LA={ i \over \hbar} [H,A]$ ...
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1answer
63 views

Time evolution of expectation value of an operator

I'm studying QM from Sakurai, and I have a doubt regarding the proof given that in the case of time independent Hamiltonian the expectation value of an observable doesn't change with time. The ...
5
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0answers
109 views

Free probability in Physics

Recently I have started reading some materials on non-commutative probability. IN this area mathematicians sometimes consider quantum theory as a non-commutative version of classical probability, with ...
0
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2answers
66 views

Intuitive interpretation of angular momentum in a macroscopic system

My professor defined the angular momentum operators in quantum mechanics as the infinitesimal rotations in the Hilbert space of quantum states. I'm looking for a qualitative, intuitive explanation of ...
4
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2answers
437 views

The curious case of the time derivative of the expectation value of the position

Having defined the expectation value of position as follows $$ \langle x \rangle = \int x {\lvert\Psi(x,t)\rvert}^2dx $$ The time derivative of the expectation value is derived in my literature in ...
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3answers
90 views

Does a magnetic field disentangle an EPR pair?

The spins of the both electrons of an EPR pair are undetermined before one conducts a measurement on one of them. Does a magnetic field determine (set up or down) the spin of one partner of an EPR ...
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1answer
55 views

Can a beam of light be modulated close to it's frequency?

I'm wondering if it would be possible to modulate a signal using photon pulses - where the frequency of the signal would be close to the frequency of the light. Also would it be possible to transmit ...
0
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1answer
64 views

Why is there no $1S_{-1/2} $ state of the hydrogen atom?

Heyho, i found this term scheme for the hydrogen atom: https://upload.wikimedia.org/wikipedia/commons/9/94/Wasserstoff_Aufspaltung.svg I was wondering why there is only a $1S_\frac{1}{2}$ state and ...
3
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1answer
135 views

Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
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3answers
221 views

How many fields that we know of permiate the universe?

The Higgs field, as I understand it reading layman's articles, permeated the entire universe only a fraction of a second after the big bang. Are there any other fields that they know about or ...
2
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2answers
81 views

A classical universe from a quantum one?

I don't understand how our quantum Universe suddenly becomes classical. If quantum mechanics governs everything - and accordingly nothing is determined - then how do we have a past history that goes ...
3
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5answers
399 views

Eigenspaces of angular momentum operator and its square (Casimir operator)

The casimir operator $\textbf{L}^2$ commutates with the elements $L_i$ of the angular momentum operator $\textbf{L}$: $$ [\textbf{L}^2, L_i] = 0. $$ However, the $L_i$ do not commute among ...
2
votes
2answers
147 views

Differences in measurement between quantum physics and classical physics?

I know that there are differences in measurement due to quantisation, probability, and collapse in quantum physics, but I am having trouble explaining how these ideas relate to measurement in an ...
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0answers
60 views

A follow up on “Double Slit Experiment in a Bubble Chamber”

The exact title is "Has a double slit experiment ever been done using a track chamber or even contemplated?". I was totally unfamiliar with the concept of the bubble chamber, so I did some amateur ...
2
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0answers
86 views

Why is the activation energy of combustion so large compared with regular bonding?

I wanted to know why combustion requires an activation energy and I found this article (see this too). It says that molecular oxygen ground state is a triplet state (according to Hund's rules), and ...
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1answer
80 views

Is it possible to plot a quantum particle's position with respect to time?

If I shoot an electron through a substance, is it theoretically possible to plot its path through said substance? Has this been experimentally done?
0
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1answer
56 views

Trapping time and site population

In thr article environment assisted quantum transport, the trapping time probability for the FMO complex, a measure of the energy transfer efficiency, is defined $2\kappa_3\int^\infty_0 dt\langle ...
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4answers
365 views

Is the uncertainty principle a statement about limits on our predictive rather than our measurement abilities?

Here's what I know. The Uncertainty Principle states that $$\sigma_x \cdot \sigma_p \geq {{\hbar} \over 2}$$ However, I also know that this principle refers to measurements performed over many ...
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2answers
99 views

How to interpret physical quantities in a superposition state?

When a spin 1/2-particle is in a superposition of spin-up and spin-down states: Should one consider the particle spin undefined in the superposition state or should one consider the particle spin ...
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0answers
31 views

Does the double split experiment set boundaries to the concept of localization?

Feynman's textbook on quantum mechanics starts with the double split experiment for single electrons, see chapter 1-5. The astonishing result is the self-interference of the single electron as long as ...
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2answers
869 views

What the lifetime of a massless black hole of photons?

Let a bundle of photons very concentrated in a very small area so that the space-time is curved as a black hole, and the photons can't escape: this is what I call a massless black hole of photons. ...
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3answers
93 views

Observing a photon during flight

When I was reading about the double-slit experiment in quantum mechanics, everything seems to make sense in terms of the waves and the interference pattern, but if thinking more about this ...
12
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3answers
1k views

Two definitions of Green's function

In literature, usually two types of definition exist for Green's function. $\hat{L}G=\delta(x-x')$. This equation states that Green's function is a solution to an ODE assuming the source is a delta ...