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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2answers
72 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?”
2
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2answers
90 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 ...
1
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1answer
52 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 ...
0
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1answer
60 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 ...
0
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2answers
38 views

Quantum entanglement thought experiment

One can "filter" a collection of electron pairs generated in an entangled (fixed-direction) spin state (e.g. singlet $\left|\uparrow \downarrow \right\rangle - \left|\downarrow \uparrow\right\rangle$) ...
0
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1answer
29 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 ...
4
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1answer
78 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 ...
6
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2answers
124 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 ...
1
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1answer
34 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 ...
0
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1answer
45 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 $l$ ...
-8
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0answers
42 views

Quantum Mechanics is not for lazy [closed]

Quantum Physics is not a subject for lazy.... How I can be an expert in Quantum Mechanics? I'm a student of Physics, currently i'm studying Quantum Mechanics as a course of mine. But, I don't ...
2
votes
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 ...
-6
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0answers
37 views

how could the sun photons be the source of light to our vision? [on hold]

if the atom has 99.99% empty space and the photon has no mass while our universe is 2dimensional flat so how could the sun photons be the source of our vision? how could photons be reflected by ...
0
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2answers
63 views

Does Quantum Collapse occur? [on hold]

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
votes
0answers
65 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 ...
0
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0answers
14 views

Transition from the second excited state to the ground state in 3d oscillator [on hold]

The problem: 3d harmonic oscillator is in a second excited state. Suddenly a perturbation is applied which depends only on the length of the position vector $|\vec{r}|$. Can the oscillator fall into ...
1
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1answer
37 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 ...
1
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0answers
47 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 ...
1
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1answer
37 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 ...
2
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1answer
34 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 ...
0
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1answer
50 views

Quantum mechanics: clarification about $S \cdot n$ [on hold]

I haven't understood what is the role of $S\cdot n$ (projection of the Spin in the $n$ direction?) in the determination of the transition probability... Could you explain me and give me an example? ...
5
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1answer
72 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 ...
0
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0answers
43 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 ...
-1
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0answers
56 views

How to find $\langle x^2 \rangle$ of a wavefunction $\psi(x,t)$ [closed]

I know how to find $\langle x \rangle$ of such a function, but I'm not sure of how to find the variance or $\langle x^2 \rangle$ of this continuous function. Any help would be greatly appreciated. ...
0
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0answers
27 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 ...
1
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0answers
31 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 ...
0
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0answers
41 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
59 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
67 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 ...
0
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1answer
64 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, ...
0
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2answers
31 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 ...
1
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1answer
39 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
55 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 $k\ll n$ ...
-3
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0answers
58 views

Singularity in the context of the Quantum mechanics [closed]

In the TV program , Professor Michio Kaku had told that singularity can be defined as the rotation of the neutron . I'm searching whether the insist was right or wrong . How does the quantum mechanics ...
0
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0answers
44 views

Lowering operator and degenerate eigenvalue [duplicate]

In this video at 5:00: https://www.youtube.com/watch?v=xniXpD3bCYU David Miller derives how the lowering operator $\hat a$ produces some wave function that has the eigenvalue $(n-1)$; thus it ...
-1
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0answers
34 views

How can we construct wavefunction using given density matrix? [closed]

I have recently learnt that for isolated systems, density matrix and the wavefunction have same information content. Given a density matrix for an isolated system, is it possible to reconstruct the ...
-2
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1answer
52 views

Probablity Wave and Wavefunction [closed]

Are wave function and probability wave same? Well I am a bit confused about wavefunctions and probability waves. I read in Fabric of the Cosmos by Brian Greene that they are same. Please help me and ...
0
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2answers
67 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 ...
6
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3answers
127 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 ...
0
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1answer
45 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: ...
4
votes
3answers
484 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} ...
1
vote
0answers
110 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: $LA={ i \over \hbar} [H,A]$ ...
0
votes
1answer
23 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 ...
-2
votes
0answers
24 views

Suggest an experiment which demonstrates that a photon must explore both paths through a beam splitter? [closed]

A left-circularly polarised photon is incident on an x-y beam splitter. Suggest an experiment that demonstrates that the photon must explore both paths through the beam splitter.
4
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0answers
68 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
36 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
228 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 ...
0
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3answers
57 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 ...
1
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1answer
42 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
votes
1answer
46 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 ...