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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A question from Coleman's Aspects of Symmetry

In Coleman's Aspect of symmetry he proposes an amusing problem in the first chapter. It asks us to consider a set of eight pseudo-scalar fields transforming in the adjoint representation of $SU(3)$. ...
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237 views

Time-dependent Schrodinger equation from variational principle

In the paper, "Density-functional theory for time-dependent systems" Physical Review Letters 52 (12): 997 the authors mentioned that the action $$ A= \int_{t_0}^{t_1} dt \langle \Phi(t) | i ...
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81 views

Integration by parts to derive $d\langle x \rangle / dt$

I am reading "Introduction to Quantum Mechanics" by David Griffiths and I am having trouble understanding part of a derivation of $\frac{d\langle x\rangle }{dt}$ in section 1.5 - Momentum - of the ...
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3answers
571 views

Why does nonlinearity in quantum mechanics lead to superluminal signaling?

I recently came across two nice papers on the foundations of quantum mechancis, Aaronson 2004 and Hardy 2001. Aaronson makes the statement, which was new to me, that nonlinearity in QM leads to ...
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51 views

Solution of the Radial Part of the Schroedinger Equation [on hold]

The general Schroedinger Equation is: $$\left[-\frac{\hbar^2}{2m}\triangle +V(r,\vartheta,\varphi)\right]\psi_{nlm}=E\psi_{nlm}$$ When considering free waves, i.e. $V(r,\vartheta,\varphi)=0$ and a ...
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Is quantum entanglement functionally equivalent to a measurement?

I saw the following talk the other day: http://www.youtube.com/watch?v=dEaecUuEqfc&feature=share In it, Dr. Ron Garret posits that entanglement isn't really that "special" of a property. He ...
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16 views

Fun physics book for high school student [duplicate]

can anyone recommend me a physics book for a highschool student (not these typical school books) a book that will let you think mostly interested in theoretical /quantum physics done with the ...
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30 views

Why Electron Does Not Radiate In Bohr Orbits? [duplicate]

Maxwell said that charged particles radiate when are in accelarating motion. I understand that $nλ=2πr$ must be fulfilled in order to create a sinusoidal standing wave and to satisfy the probability ...
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1answer
41 views

Quantum computing can be done via measurement alone, why is this significant?

I read in the Afterword section of Nielsen and Chuang's book Quantum Computation and Quantum Information that A second area of progress has been in understanding of what physical resources are ...
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1answer
93 views

How to visualize a Schrödinger cat state?

I recently read about Schrödinger cat states (SCS), which are basically a superposition of two coherent states $|\alpha\rangle$ with opposite phases, that is, $$ |cat\rangle = |\alpha\rangle \pm ...
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1answer
27 views

Preventing Heat Escape

Is is possible to completely prevent heat from escaping from a closed container? Here is a diagram of vacuum flask, which tries to implement the design - Vacuum Flask prevents heat from escaping ...
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4answers
87 views

Can a photon have little to no energy and/or speed?

Can a photon move more slowly than the speed of light and behave 'non-relativistically,' so to speak. Perhaps another way to express my thought is: could we stop a photon from moving?
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337 views

Hubbard Model Hamitonian

$H = -\sum\limits_{i,j} A_{ij} c_i^{\dagger} c_j + \frac{U}{2} \sum\limits_i(c_i^\dagger c_i)(c_i^\dagger c_i -1)$ is defined to be a Hamiltonian for modeling quantum random walk of identical ...
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1answer
253 views

Why is the orbital angular momentum of a pi electron along the axis of two atoms' molecule one?

I'm reading quantum chemistry. The book says that the orbital angular momentum of a $\pi$ electron along the symmetry axis of a molecule made up of two atoms is $\pm 1$. I think this is a primary ...
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51 views

Probability flux

I was reading a text on Quantum Mechanics in which it said that $$\int{d^3 x \, j(x,t)} = \frac{\langle p\rangle}{m},$$ where $\langle p\rangle$ is the expectation value of the momentum operator at ...
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1answer
93 views
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Approximating a target operator

I was wondering if anyone knew how the author got to equation 12 on page four of this paper, I will attempt to explain the situation below. Given $C$, a target operator, we wish to create an ...
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2answers
148 views

Quantum mechanics and the atom

I was thinking about the nature of the atom, specifically, why electrons do not spiral into the nucleus. My physics book says the principal quantum number $n$ must be an integer number of wave ...
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4answers
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What is spin as it relates to subatomic particles?

I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does ...
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1answer
72 views
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What is the significance of being equivalent up to local isometry?

Background : I am reading the paper device independent outlook on quantum mechanics. The author mentions the concept of two pure states being equivalent up local isometry. From what I understood two ...
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5answers
830 views

Commutator algebra in exponents

Considering $X$ and $Y$ such that $[X,Y]=\lambda$, which is complex, and $\mu$ is another complex number, prove: $$e^{\mu(X+Y)}=e^{\mu X} e^{\mu Y} e^{-\mu^2\lambda/2}$$ My attempt (so far) is: ...
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1answer
53 views

Does new energy creation exist?

I know that basic physics states that energy cannot be created or destroyed, but why is that true? For example, one theory called Quantum Fluctuation states that 'normal' and anti energy is constantly ...
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4answers
65 views

Do the interference terms disappear really after decoherence?

I was reading decoherence from this site, where I found the following bold words which states that the out-of-phase components do not really get dissappear after decoherence: What happens to a ...
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2answers
45 views

Direct definition of density of states

I've been studying statistical mechanics and in the book there's something the author calls density of states which he introduced in a kind of indirect way. Basically, the author argues that if we ...
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45 views

Why we need to suppose the chemical potential is zero here?

I've been working on some statistical mechanics problems and one of them asks to compute the pressure with chemical potential zero of a boson gas whose particles do not interact and whose energies are ...
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1answer
162 views

Are the authors saying that the observer effect plays no role in Bohr's thought experiment of the Heisenberg uncertainty principle?

Here is an excerpt from Eisberg & Resnick's Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. Here is introducing Bohr's though experiment to establish a physical origin for the ...
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39 views

Possible values of an observable are the eigenvalues of an operator

Ok, so I'm beginning to study quantum mechanics. For reference, the book I'm using is "Konishi-Paffuti/Quantum Mechanics-A New introduction". Now, I get that the quantum state of something (say, a ...
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33 views

Measuring the spin of an electron with spin +h/2 at an axis 30 degrees off [closed]

The problem: If the z component of an electron spin is $+\hbar/2$, what is the probability that its component along a direction z' that forms an angle $\theta$ with the z axis equals $+\hbar/2$ or ...
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1answer
43 views

Relation between Von Neumann entropy (and other entanglement measures) and thermodynamical entropy

Suppose I have a bipartite system (with Hilbert space $H = H_a \times H_b$) and the following state: $$\sigma = \sum_{n} \frac{e^{-\beta E_n}}{Z} \rho_n$$ where $Z = \sum_n e^{- \beta E_n}$ and ...
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2answers
107 views

Uncertainty principle in quantum field theory

Can the uncertainty principle be derived in quantum field theory? If yes, does is have a different interpretation than quantum mechanics because the coordinates $x_i$ are now parameters and not ...
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1answer
88 views

Probability current in scattering problems

This is a section from Wikipedia: In regions where a step potential or potential barrier occurs, the probability current is related to the transmission and reflection coefficients, respectively ...
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6answers
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How is quantum superposition different from mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now consider state ...
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63 views

Why do particles and antiparticles annihilate? [duplicate]

I was wondering about this and I would like to know an explanation why do particles and antiparticles annihilate? I would be interested in phenomenological, but most importantly mathematic explanation ...
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22 views

Can we say that pressure obeys this relation?

I've been studying statistical mechanics and quantum ideal gases, and there's one exercise on the book which says the following: Consider one free particle inside one three-dimensional box with ...
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1answer
198 views

First order coherence through double slit

The state $$|\Psi \rangle = |0\rangle + \sum_j \int d\omega f_j(\omega)\hat{a}^\dagger_j (\omega) |0\rangle $$ is coming from a far field and incident on a double slit setup. Here j is the index of ...
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42 views

Electron energy in magnetic field

For a problem early in a book I'm reading (Quantum Mechanics by Albert Messiah), I'm asked the following: Consider an electron following a circular trajectory in a constant magnetic field $H$ (I'm ...
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2answers
87 views

Is every bra vector the complex conjugate of ket vector?

$\renewcommand{\ket}[1]{\lvert #1 \rangle}\renewcommand{\bra}[1]{\langle #1 \rvert}$Suppose we are taking the inner product of two vectors, say $a$ and $b$ as $$\bra{a}b\rangle$$ where $\bra{a}$ is a ...
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883 views

Why are eigenfunctions which correspond to discrete/continuous eigenvalue spectra guaranteed to be normalizable/non-normalizable?

These facts are taken for granted in a QM text I read. The purportedly guaranteed non-normalizability of eigenfunctions which correspond to a continuous eigenvalue spectrum is only partly justified by ...
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4answers
281 views

Is it possible for two events happen at the exact same time?

Is it possible for any two thing to occur at the exact same time? As I see it, because time can always be split up into smaller units (it is infinitely divisible), we can always be more and more ...
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1answer
33 views

How is measurement on system in a Hilbert space seen?

I am a bit confused about different kinds of measurements on a system in state $W$ where $W$ is the density operator in Hilbert space $H$. A general measurement can be given by POVM's, let ...
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1answer
44 views

Property of the wave functions of a free particle

How can I show that the following holds? $$\langle nlm\mid \partial_z^2\mid nlm\rangle=-\int_0^{4\pi}d\Omega\int_0^{\infty}drr^2\left|\partial_z\psi_{nlm}\right|^2$$ The wave functions of a free ...
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24 views

Time dependence of the displacement operator

I am following the derivation of the master equation (and application of this) in these lecture notes. Unfortunately I do not follow the step of eliminating the driving terms of the harmonic ...
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0answers
18 views

Can I use the Chi squared test to see if my data fit to the Wigner-Dyson distribution indicating chaotic behaviour?

I recently read the paper about Quantum Chaos in Feshbach resonance spectra of ultracold Erbium [1]. The authors analyze their data statistically using the random matrix theory framework for ...
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20 views

Why is it necessary for all the component-states to have same phase for interference?

I am currently reading Decoherence. In this site, it is written : Now here is the absolutely key point: every component eigenstate has an associated phase . It is this phase$^1$ which gives the ...
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4answers
342 views

Seeking a quality plain-language description of the Wigner-Eckart theorem

I'm a third year physics undergrad with a very cursory knowledge of quantum mechanics and the formalism involved. For instance, I understand roughly how tensors work and what it means for a tensor to ...
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3answers
133 views

What can change a photon's frequency?

I found this question: Is it possible to apply force to a light particle? As it states, gravity can change the frequency of light by changing its momentum. My question regards other phenomena that ...
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2answers
108 views

Time evolution of a wavepacket

I do not understand why if $H\psi = E\psi$, then the time-evolution of the wavefunction is given by $e^{-iEt/h}\psi(x)$.
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408 views

Why doesn't Many-Worlds interpretation talk about many worlds?

I was reading this interpretation from this site, where these lines are noteworthy enough to talk for the fact that this interpretation doesn't actually talk about many-worlds: These are the "many ...
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2answers
282 views

Many-worlds interpretation vs 'just' randomness?

I have this question about MWI I always wanted to ask but never dared to! It could be that I just don't know enough physics to understand the answer, or the question! Anyway, here goes: What is it ...
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28 views

Position operator for wave function of entangled system? [on hold]

When I read about EPR paradox, I have the following confusion. Consider the whole system, it is a pure state, so it can be described by a wave function. (For sub-system(one of the electrons), it is ...
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1answer
104 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 ...