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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On LOCC operations

I am trying to learn quantum information theory. Suppose we have a bipartite (as well as multi-partite) quantum system $H_A \otimes H_B$. What is a LOCC map $\phi: \mathcal{B}(H_A \otimes H_B) \...
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0answers
25 views

Are Fock spaces just a special type of tensor algebra?

Are Fock spaces just a special type of tensor algebra? The definitions I am using: http://en.wikipedia.org/wiki/Fock_space http://en.wikipedia.org/wiki/Tensor_algebra From what I can tell, the ...
5
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1answer
142 views

How to calculate the ground states' Berry phases with doubly degeneracy, such as that due to the particle-hole symmetry or time reversal symmetry?

Suppose the ground states of a system are doubly degenerate due to an anti-unitary symmetry $K$, which are $|\psi>$ and $|K\psi>$. If the system is an one-dimensional Fermion system and anti-...
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0answers
20 views

Eigenkets in matrix representation

We use base kets in matrix representation of an operator $X$. Could the base kets be possibly be eigenkets also, of operator X? (Here, I'm taking X as a general operator , not only observable,i.e. ...
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3answers
3k views

Do protons exchange photons with electrons?

I'm sorry for this question but, I just don't get it. According to the electromagnetic field theory, electrons repel each other by exchanging photons. How do protons attract electrons, by photon ...
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3answers
552 views

Quantum Mechanics in Electric Field

I am working on a problem which looks like this. Consider a charged particle with charge $q$ trapped in a box of length $L$ with finite constant potential $ V_0 $ on both ends. A constant (static) ...
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1answer
39 views

Communication via teleportation/entanglement (FTL communication)

I know this has been asked many times, but I have a hard time "crystallising" it in my mind. First: let's say we teleport a DVD (with quantum teleportation). Isn't this FTL communication? Second: ...
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0answers
30 views

How to do partial trace of three qubit? [on hold]

Good day, $\|A\rangle=\left(\dfrac{i_0}{j_1}\right)$, $\|B\rangle=\left(\dfrac{i_0}{j_1}\right)$, $\|C\rangle=\left(\frac{i_0}{j_1}\right)$, For 2-qubit systems, the $\|AB\rangle\langle AB|$, ...
8
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1answer
688 views

Many-worlds: Where does the energy come from?

With regard to the theory that each time a wave function collapses the universe splits so that each possible outcome really exists - where does all the energy required to create all the new universes ...
2
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2answers
127 views

What is the correct quantization of Hamiltonians of the form $H=x·p$ whose naive quantization is not Hermitian?

As we all learn in Basic Quantum Mechanics (the first quantization), we promote the classical variables to operators. Say, the classical hamiltonian $\frac{p^2}{2m}+V(x)$ to $-\frac{\hbar^2}{2m}\frac{...
2
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1answer
140 views

Thermionic emission, delayed emission and predissociation

In molecular photodissociation, the thermionic emission, delayed emission and predissociation are the same? Otherwise, what is the difference between them? My question is not about the solids, but I ...
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0answers
23 views

Balancing a Quantum mechanical pencil [duplicate]

I have tried to solve the question given in Sakurai quantum mechanics book about what is the maximum time you can balance a pencil on its tip using the uncertainty principle. Classical pencil is in ...
1
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1answer
130 views

Excitation energy of carotene using the particle in a box model

I'm practicing for an exam and I came across the following question: The linear, conjugated π-electron system of a carotene molecule comprises 11 atoms and the distance between two atoms is 1.4 Å. ...
5
votes
2answers
75 views

Uncertainty Relations, Conjugate Quantities, and Fourier Transforms

I've heard from a lot of people that the reason momentum and position have an uncertainty relation is because of the Fourier Transform. But is this in any way the case? If it were I would expect all ...
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2answers
166 views

Does quantum randomness measurably affect macro-sized objects?

I understand that while it is believed that there is no true randomness on the macro scale, there is true randomness on the quantum scale. A previous theory that quantum processes could be determined ...
0
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1answer
23 views

Potential step and tunnelling

Imagine a particle with energy $E$ heading towards a potential step with height $V_0$ where $E<V_0$. The particle's wave function is oscillatory before the boundary and exponentially decaying in ...
3
votes
2answers
46 views

Moving of spin up and spin down electrons in a magnetic field

Suppose we have an electron in a conducting space, and now we apply a magnetic field. Now according to the right hand rule, the electron will have a circular motion in the plane perpendicular to the ...
0
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0answers
26 views

Can we see interference if move screen? [on hold]

In interference using electrons in double slit experiment, we cannot use light source, as it disturbs apparatus. But, can't we simply move screen towards and away from screen, to know where they ...
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4answers
1k views

What does the Schrodinger Equation really mean?

I understand that the Schrodinger equation is actually a principle that cannot be proven. But can someone give a plausible foundation for it and give it some physical meaning/interpretation. I guess I'...
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2answers
39 views

What is a magnetic line of force?

Do magnetic limes of force 'flow'? If so, what is it that is flowing? What is the 'line of force' composed of?
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0answers
18 views

Uncertainty principle-QM [duplicate]

I some trouble understanding the uncertainty principle. I understand most of the math derivation but not the physics. Is there any intuitive explanation of this idea, and why is the uncertanty does ...
0
votes
1answer
43 views

State vector after quantum eraser

Suppose I have a particle in a two-slit setup. At the slits, it's in state $|\psi\rangle = |x_1\rangle + |x_2\rangle$ I entangle it with some detector: $|\psi'\rangle = |x_1\rangle|d_1\rangle + |...
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3answers
39 views

Two qubits system in polar co-ordinates

I know that I can write a single qubit state in terms of polar co-ordinates $(r,\theta,\phi)$ on a Bloch sphere. \begin{equation} \rho = \begin{pmatrix} \frac{1+r \cos\theta}{2} &\frac{r \exp(-i\...
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2answers
2k views

Pauli matrices as measurement operators

I am trying to understand a paper on the Bell test experiments. I understand that if we wanted to measure the spin of a spin-1/2 particle in state $\psi$ along the z-axis we would apply the operator $...
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0answers
51 views

Generalisation of a particle in QFT

In classical mechanics, we assumed a particle to have a definite momentum and a definite position. Afterwards, with Quantum mechanics, we gave up the concept of a time-dependend position and momentum, ...
6
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2answers
3k views

If randomness doesn't exist, how come the universe isn't a perfect sphere with predictable distribution of matter?

I'm presuming that the scientific community pretty much agrees that randomness doesn't exits, and that everything has a cause. Please correct me if I'm wrong, I've heard of quantum mechanics, but as ...
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9answers
6k views

Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in this video. However, I wonder; is this actually a duality? ...
4
votes
1answer
129 views

Coherent states and completeness

Consider one possible definition of a Gaussian (coherent) state in the position representation $$ \langle r | \psi(r_i,p_i) \rangle = \left( \frac{ 2 \gamma}{\pi} \right)^{\frac{1}{4}} \exp \left[ -\...
6
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2answers
142 views

Why hermitian, after all? [duplicate]

This question is going to look a lot like a duplicate, but I've read dozens of related posts and they don't touch the subject. Here we go. Why are observables represented by hermitian operators? ...
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3answers
266 views

Can we predict throwing a dice?

What happens if we throw a dice from same position, with same force, by creating a vacuum environment on earth? Will it be predictable now i.e. will the dice have same results all the time? If answer ...
2
votes
2answers
47 views

Does QFT modifies Quantum Mechanics? [duplicate]

The basis of Quantum Mechanics is contained in the postulates which tell us how to describe quantum systems (below I disconsider possibly degenerate spectra just for simplicity): To describe a ...
0
votes
2answers
153 views

General formula for expanding wave function in terms of orthogonal states?

Given a wave function $\psi(x) = \langle \psi | x \rangle$. It can be expanded in terms of orthogonal states: $$ \langle \psi | x \rangle = \sum_n \langle \psi | n \rangle \langle n |x \rangle $$ ...
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0answers
10 views

Spin half particle Magnetic field oriented along y-axis

I've been looking over past papers for an upcoming QM exam and have had a few issues wrapping my head around this question. I can follow the common example as seen in Griffiths where the field is ...
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1answer
45 views

What does coherent superposition mean?

There is only one coherent state: $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle $$ Also, a pure state does not mean a coherent state. But when does ...
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2answers
39 views

In quantum double slit experiment what is the state vector or density matrix of the electron after the electron passes through the two slits?

Also I would like to confirm my thinking on quantum double slit experiment. Before it passes through the two slits (slit 1 and slit 2), is the electron state vector $\frac{1}{\sqrt{2}}\left(\left|...
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0answers
28 views

Luminiferous æther = quantum's “vacuum”? [on hold]

How is the luminiferous ether, which relativity theory disregarded, different from and similar to what in quantum mechanics is called "the vacuum"?
3
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2answers
123 views

Proton and electron joining

If I have a proton and an electron at rest at some distance apart. Will they form an hydrogen atom when released or they will join together? My intuition says it will form H atom. But I cannot ...
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0answers
31 views

Interpreting conical intersection in quantum adiabatic evolution

Recently, I have studied a particular quantum adiabatic algorithm. When I plot the eigenvalues of the ground and first excited state against normalized time $s$, there appears a conical intersection. ...
1
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1answer
17 views

Out-of-plane electronic band structure for 2D materials?

There's been much recent interest in 2D materials since they can form monolayer-thick films. Since their crystal structure is periodic along the in-plane directions, the electronic band structure ...
2
votes
1answer
112 views

Simplest Live Demonstration of Adiabatic Transport

I have to give a presentation on Berry phase. I would like to give the simplest live demonstration of adiabatic transport. If I move an object in a loop and return that object back into its original ...
4
votes
2answers
488 views

double slit experiment with two opposite quarter waveplates

Consider the usual double slit experiment involving laser and a double slit and a screen. Now place in front of the left slit a quarter waveplate (let's call it QWP1) that changes a certain linear ...
0
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1answer
42 views

Macroscopic quantum coherence in classical electromagnetic field [duplicate]

In quantum coherence wikipedia article "Regarding the occurrence of quantum coherence at a macroscopic level, it is interesting to note that the classical electromagnetic field exhibits macroscopic ...
0
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0answers
35 views

Why Does the Dirac delta Function Fix the Normalization of the Basis Vectors in Infinite Dimensions? [duplicate]

On page 60 of Shankar's intro to QM at the very bottom he says that the Dirac delta function fixes the normalization of the basis vectors with an infinite amount of dimensions. I don't understand why ...
0
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1answer
24 views

Why can the 2p0 to 1s transition in hydrogen with dipole interaction not be solved without splitting into x,y,z polarisation?

The $2p_0$ and $1s$ wavefunctions for hydrogen; $ \psi_{2p_0} = \dfrac{1}{4\sqrt{2\pi}} \left(\dfrac{Z}{a_b}\right)^{\frac{3}{2}} \dfrac{Z r}{a_b} e^{\frac{-Zr}{2a_b}} \cos(\theta) $ $ \psi_{1s} = ...
3
votes
1answer
151 views

Can different components of a wavefunction become entangled with different systems?

Imagine a $z$-basis spin Stern Gerlach experiment where a single particle is put through the apparatus. The output is a spin state vector consisting of the sum of the two $z$-spin states. Each spin ...
0
votes
1answer
30 views

Bohr frequency of an expectation value?

Consider a two-state system with a Hamiltonian defined as \begin{bmatrix} E_1 &0 \\ 0 & E_2 \end{bmatrix} Another observable, $A$, is given (in the same basis) by \begin{bmatrix} 0 &a \...
2
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1answer
48 views

Basis/Projection Notation Question Quantum Mechanics

Lets say you have a inner product between two state vectors with an operator in between A|X|B. I can write this as a summation over I and j as A|i i|X|j j|B (sorry for notation). But I don't ...