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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What does the Coleman-Mandula theorem state exactly?

I have read about the Coleman-Mandula theorem in quantum field theory. This is a theorem that makes some restrictions to the gauge group generators $T^a$. What are precisely the restriction on the ...
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22 views

how to solve the following question about quantum mechanical wave function?

How to solve this question regarding quantum mechanical wavefunction ?
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1answer
5 views

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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1answer
44 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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1answer
49 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
50 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
38 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
31 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
53 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
32 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
24 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
66 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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85 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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26 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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19 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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40 views

Quantum Mechanics is not for lazy [on hold]

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 ...
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1answer
57 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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32 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 ...
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2answers
57 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 ...
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55 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 ...
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13 views

Transition from the second excited state to the ground state in 3d oscillator

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 ...
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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 ...
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45 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
35 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
21 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 interesting, ...
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1answer
49 views

Quantum mechanics: clarification about $S \cdot n$

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? ...
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1answer
68 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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37 views

Can a density matrix be complex?

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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1answer
64 views

Can some one explain about m theory? [on hold]

I am very new to m theory and string theory. I am very through with classical physics and little bits of quantum mechanics. Will you be able to explain why the fact that gravity is a week force being ...
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48 views

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

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. ...
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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 ...
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26 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 ...
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31 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 ...
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1answer
56 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
66 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
61 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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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 ...
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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 ...
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66 views

Are we teleporting? [on hold]

First of all - i'd like to declare that i'm a complete and utter noob when it comes to anything physics or mathematics involved.So please be patient with me and explain everything to me in layman's ...
2
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1answer
53 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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55 views

Singularity in the context of the Quantum mechanics [on hold]

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 ...
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40 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 ...
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0answers
33 views

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

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 ...
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1answer
48 views

Probablity Wave and Wavefunction [on hold]

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 ...
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2answers
63 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
110 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
39 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
467 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} ...
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97 views

Quantum Liouville-Propagator Operator Trace Identity [on hold]

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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22 views

Calculation of lowest energy [closed]

5 spin 1/2 particles are under an 1D harmonic oscillator potential.What is the lowest energy states of the system? I primarily tried it considering no degeneracy of any eigenstates.But I got it wrong. ...