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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spectral eigenvalue staircase and quantum system

in a d-dimensional system of Quantum physics , does the Eigenvalue staircase $ N(E)= \sum_{E_{n}\le E} 1 $ determine ALL the properties of Quantum System ?? for example, let us assume that the ...
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Help me understand the first equation in Landau & Lifshitz's Quantum Mechanics

While I've covered a basic course in Quantum Mechanics, I'm self-studying Landau & Lifshitz's book to help me understand what's going on. Unfortunately, I'm stuck on the very first equation in ...
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Are Quantum Physics and statistical theory always the same as semiclassical approximations?

Quantum Mechanics and Statistical physics is a bit hard , could we then study only the WKB approximation ? In the form: replace $ \sum_{n=0}^{\infty}exp(- \beta E_{n})=Z(\beta)\sim\iint ...
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Why does photon have only two possible eigenvalues of helicity?

Photon is a spin-1 particle. Were it massive, its spin projected along some direction would be either 1, -1, or 0. But photons can only be in an eigenstate of $S_z$ with eigenvalue $\pm 1$ (z as the ...
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Does the Hilbert space of the universe have to be infinite dimensional to make sense of quantum mechanics?

Does the Hilbert space of the universe have to be infinite dimensional to make sense of quantum mechanics? Otherwise, decoherence can never become exact. Does interpreting quantum mechanics require ...
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On Bolte's semiclassical law

i have seen on internet the following, for $ E >> 1 $ the Eigenvalue Staircase can be approximated by $ N(E)= \frac{1}{\pi}argZ(1/2+i \sqrt E ) $ ...
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Geometry as Physics [closed]

What would be good introductory and follow-up references to understand the close ties between physics and geometry. I'm a retired engineer with the math background to handle Shankar's Principles of ...
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Known properties of a specific class of quantum states

Recently, I have been studying a quantum protocol for the "Hidden Matching" problem that makes use of states that can be expressed as $|\psi\rangle=\frac{1}{\sqrt{n}}\sum_{i=1}^n ...
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223 views

What counts as a measurement?

In quantum mechanics, an elementary particle does not have a well defined position until a measurement is performed on it (right?). Such a "measurement" is any sort of interaction with other ...
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339 views

Set theory, category theory, realism and the recent “reality of the wavefunction” papers

I will add a better phrased question here. Do we need to consider quantum foundations to form a quantum theory of gravity? The kind of foundational question I am thinking of is expressed in the ...
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Why does spin have a discrete spectrum?

Why is it that unlike other quantum properties such as momentum and velocity, which usually are given through (probabilistic) continuous values, spin has a (probabilistic) discrete spectrum?
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Operators and Commutator Definitions

I have several problems with General Definitions of an Operator and Commutator : the product of operators is generally not commutative: $$\hat A \hat B \not= \hat B\hat A .$$ what is this means ...
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Intuitive explanation for the de Broglie / Planck relations

A friend asked me to explain "why" a particle's energy is proportional to it's frequency, i.e: $$E=h\nu$$ The reason this result is so un-intuitive, is that in the macroscopic world, A wave's energy ...
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quantum explanation of doppler effect

How would quantum mechanics explain doppler effect? And just for curiosity, is there any effect similar to doppler effect occuring at quantum level?
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353 views

interpretation of Green function

Is there a physical interpretation of the existence of poles for a Green function? In particular how can we interpret the fact that a pole is purely real or purely imaginary? It's a general question ...
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181 views

Observationally indistinguishable quantum states

What does it mean for 2 quantum states to be "observationally indistinguishable"? If I may venture a guess: Does that mean that the set of possible measured values are the same though the ...
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130 views

Can we develop in the future a technology that can send a message to the past? [duplicate]

Possible Duplicate: Is it possible to go back in time? I believe that everything is possible in this world. If that can be done then why aren't we receiving any message from the future.
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381 views

Show quantum entanglement to a classical thinker

Can someone describe a simple experiment to convince a person thinking about physics classically (called Claus) that quantum mechanics has something weird, entangled? I mean an experiment that he ...
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Adding 3 electron spins

I've learned how to add two 1/2-spins, which you can do with C-G-coefficients. There are 4 states (one singlet, three triplet states). States are symmetric or antisymmetric and the quantum numbers ...
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Apparent contradiction between calculations and intuition?

I am rather confused because it would seem that mathematical conclusions I have drawn here goes against my physical intuition, though both aren't too reliable to begin with. We have a potential step ...
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A two-level system absorbs a detuned photon. Where does the extra energy go?

Let's consider simple two-level system with frequency gap of $\omega_0$ between ground and excited state. Now, when we turn on external electromagnetic field with frequency $\omega < \omega_0$, ...
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Deriving Statistical Mechanics laws from Quantum Mechanics?

Since the law of individual molecule is governed by Quantum Mechanics, and the interaction of large number of molecule is governed by Statistical Mechanics, can we derive Statistical Mechanics from ...
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375 views

Why is there a phase factor when the two composite angular momentum is exchanged in Clebsch–Gordan coefficients

An identity exists for CG coefficients: $$\langle j_1 m_1 j_2 m_2 |J M \rangle = (-1)^{j_1+j_2-J} \langle j_2 m_2 j_1 m_1|J M\rangle,$$ But why is there a phase factor $(-1)^{j_1+j_2-J}$? It seems ...
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Is resonating valence bond (RVB) states long-range entangled?

Quantum liquid is at the core of condensed matter theory study, examples include superfluid in Bose Hubbard model, quantum spin liquid around the RK point of a quantum dimer model, string-net ...
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boundary conditions

Consider the following operator: $ -i\hbar x\frac{df(x)}{dx}-i\hbar \frac{f(x)}{2}=E_{n}f(x)$ What kind of boundary conditions can I enforce? I have tried to find a function such that for every ...
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What is spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
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simulate a quantum computer on a normal one

Would it be possible to simulate a quantum computer on a normal computer. I was thinking something like have a bunch of GPU's running a set of entangled quantum particles and then produce the results. ...
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what is phase angle of wave function $\phi \,$?

this is wave function: $$\Psi{(\vec r, t)}=\Psi_0 e^{i(\vec k \cdot \vec r-\omega t)}$$ $$\Psi{(\vec r, t)}=A e^{i(\phi + \vec k \cdot \vec r-\omega t)}$$. what is phase angle $\phi$ of wave ...
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Which equation tells you the minimum energy of a wave needed to see a small particle?

I have a problem that asks for the minimum energy of a wave that we will use to see a particle of size $.1\text{ nm}$. I understand that I can not see a $.1\text{ nm}$ particle with any wave length ...
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611 views

Conversion from natural units to SI

I got questions about converting units from natural system of units to SI. To be exact, I'm solving the problem in Heisenber interpretation of quantum mechanics, and I'm using Heisenberg equation of ...
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337 views

Commutators with a density matrix

The equation describing the evolution of our system is as follows: $ \dot{\rho} = u_1(t)(a^\dagger a \rho - 2a\rho a^\dagger +\rho a^\dagger a) + u_2(t)(a a^\dagger \rho - 2a^\dagger\rho a +\rho a ...
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624 views

Where can I find beginner's information about quantum mechanics? [duplicate]

Possible Duplicate: Popular books on QM I hope that this question is suitable for this site. I am interested in reading up on quantum theory so that I can reasonably understand the ...
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222 views

What is behind recoherence?

I am quite familiar with the concept of decoherence, and I heard that a system that has decohered could recohere after that, I was wondering what could cause the the coherences that have leaked into ...
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Is quantum entanglement an objective or subjective property?

Imagine the following gedankenexperiment. Observer Alice is right here on Earth. Observer Bob is at say Alpha Centauri. A pair of maximally entangled qubits is formed with one qubit handed over to ...
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How can a Photon have a “frequency”?

I picture light ray as a composition of photons with an energy equal to the frequency of the light ray according to $E=hf$. Is this the good way to picture this? Although I can solve elementary ...
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Any link between decoherence and renormalization?

I have been studying decoherence in quantum mechanics (not in qft, and don't know how it is described there) and renormalization in QFT and statistical field theory, I found at first a similarity ...
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206 views

Examples of piecewise smooth dynamical systems [closed]

I have recently been studying continuous dynamical systems whose phase space can be divided into a number of regions. Inside each of these the flow is smooth, but there is a discrete jump in the flow ...
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3answers
880 views

$\hbar$, the angular momentum and the action

Is there anything interesting to say about the fact that $\hbar$, the angular momentum and the action have the same units or is it a pure coincidence?
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1answer
647 views

Work done on charged particle by magnetic field in quantum mechanics

Classically, we know from $\mathbf{F}=q\mathbf{v}\times \mathbf{B}$ that magnetic field does no work on a charged particle. In quantum mechanics, the Hamiltonian of a charged particle in a magnetic ...
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147 views

Variational wavefunctions and “spread” of potential in quantum mechanics

A particle in a box has an energy that decreases with the size of the box. In the general case, it is often said that a variational solution for a "narrow and deep" potential is higher in energy than ...
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555 views

How Represent Waves via Complex Numbers?

i try to finished my thesis, (Just have a problem with the wave mechanics) this is wave function: $$\Psi(\vec x, t)=A\exp{i(\phi+\vec k.\vec x-\omega t)}$$ In mathematics, the symbol $i$ is ...
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300 views

Change In Momentum In Uncertainty Principle

The most basic explanation for the Heisenberg Uncertainty Principle is that the momentum and position of a quantum particle is not very distinct when an attempt is made to measure them together. But ...
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Are there any connections between James–Stein estimator and quantum mechanics?

Very nice statement from wiki: When three or more unrelated parameters are measured, their total MSE can be reduced by using a combined estimator such as the James–Stein estimator; whereas when ...
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Supersymmetry in Quantum Mechanics

I was reading Supersymmetry in Quantum Mechanics and got stuck in the various mathematical terminology like "Graded-Lie Algebra", "Super Algebra". Is there any good lecture notes concerning these ...
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544 views

Wick rotation and the arrow of time

It is well known that we can switch from a statistical system to a quantum mechanical system by a Wick rotation. Has this rotation some implication on the way the time flow? namely, this is an ...
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Time Reversal Invariance in Quantum Mechanics

I thought of a thought experiment that had me questioning how time reversal works in quantum mechanics and the implications. The idea is this ... you are going forward in time when you decide to ...
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1answer
372 views

Proof of adiabatic theorem on Wikipedia

I'm having trouble following the proof of the adiabatic theorem (apparently due to Messiah) on Wikipedia. At one stage we have: $U(t_1,t_0)=1+{1\over i}\int_{t_0}^{t_1}H(t)dt+{1\over ...
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What does it mean that particles are the quanta of fields?

I saw the question What are field quanta? but it's a bit advanced for me and probably for some people who will search for this question. I learned QM but not QFT, but I still hear all the time that ...
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224 views

What exactly does $S$ represent in the CHSH inequality $-2\leq S\leq 2$?

What exactly does $S$ represent in the CHSH inequality $$-2~~\leq ~S~\leq ~2?$$ Sorry I've been reading for a couple days and I can't figure out what exactly $S$ is and the math is a bit over my ...
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Quantum Entanglement - Measuring Twice

In the answer here and on the wiki article and many other articles it is mentioned that if one of 2 entangled particles is measured their state collapses according to the Copenhagen interpretation. ...