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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903 views

The implication of anti-commutation relations in quantum mechanics

All the textbooks I saw are very clear about the implications of commutating operators in quantum mechanics. However, much less is said about anti-commutation relations. Does it have a general ...
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8answers
1k views

Why do quantum physical properties come in pairs?

Why do quantum physical properties come in pairs, governed by the uncertainty principle (that is, position and momentum?) Why not in groups of three, four, etc.?
2
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1answer
695 views

“Completeness” of eigenvectors in a complete, commuting set

This question was originally the one below dashed line. Now after further discussions, it has boiled down to this question: Is the following construction possible? Suppose we have a 3 dimensional ket ...
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2answers
346 views

Momentum Energy and Higgs

So, as an object accelerates it gains energy. And energy is mass. So an object becomes more massive as it approaches the speed of light. But, if mass is ONLY due to an object's interaction with the ...
3
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1answer
345 views

Higgs Field compared to EM field

So, I've been reading about the Higgs because of all of this excitement lately with the LHC. I'm just a layman in physics but one thing I understood was that the Higgs field permeates all of space ...
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2answers
150 views

Can quantum measurement process be thought of as a sieve?

Consider an observable represented by the Hermitian operator $$A=\sum_{a'}a' |a'\rangle \langle a'|.$$ As I read on Sakurai's textbook, the process of measuring $A$ throws a system ...
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2answers
372 views

Einstein's Mass-Energy Equivalence versus Quantum Kinetic Energy

Using a naive view of Einstein's Energy Mass Equivalence $E=mc^2$ (where m is mass and c is the speed of light), it seems tempting to interpret this as a quantum mechanical version of the inherent ...
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1answer
255 views

Numerical algorithms to generate a random wavefunction from a thermal ensemble

I am seeking an algorithm to generate a random wavefunction = $\sum {c_i |\varphi _i\rangle }$ from a thermal ensemble, whose density matrix $\rho \sim e^{-\beta H}$, without the need to diagonalize ...
5
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1answer
377 views

Time-ordering vs normal-ordering and the two-point function/propagator

I don't understand how to calculate this generalized two-point function or propagator, used in some advanced topics in quantum field theory, a normal ordered product (denoted between $::$) is ...
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2answers
139 views

What are some examples of how the discovery of dark energy can impact other, seemingly unrelated, branches of physics?

We know that dark energy is leading to the accelerating expansion of the universe and therefore determines the ultimate fate of our universe, but what other implications might it have on physics and ...
2
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2answers
188 views

Can the implications of dark energy be used to bridge the gap between Quantum Mechanics and General Relativity?

Can the findings of the Physics Nobel Laureates of 2011, namely the overpowering existence of dark energy (vacuum energy) have any implications in the quest the combine Quantum Mechanics and General ...
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1answer
395 views

Pauli Matrices in orthogonal space

In some literature there is reference to $\tau$ matrices which are the same pauli matrices in an orthogonal space. I have not seen any explicit constructions of this anywhere. Could someone tell me or ...
3
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1answer
775 views

How to write the Fröhlich Hamiltonian in one dimension?

I am currently working on a (functional) analysis problem refining Pekar's Ansatz (or adiabatic approximation, as it is called in his beautiful 1961 manuscript "Research in Electron Theory of ...
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1answer
264 views

Crystal Field Theory

I am literally lost with this question: Suppose that within the set of (2L+1)(2S+1) lowest-lying ionic states the crystal field can be represented in the form a(L_x)^2 + b(L_y)^2 + c(L_z)^2, with ...
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1answer
108 views

Is the Energy Sharply or Fuzzily Defined in Quantum Mechanics?

According to quantum mechanics, energy of a state is uncertain within a small range in hydrogen atom. But we also know that energy of a state is quantized which is contradictory to the first. Which ...
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2answers
2k views

Sinusoidal vs exponential wave functions with Schrodinger's equation

When solving Schrodinger's equation, we end up with the following differential equation: $$\frac{{d}^{2}\psi}{dx^2} = -\frac{2m(E - V)}{\hbar}\psi$$ As I understand it, the next step is to guess the ...
4
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2answers
492 views

How is the Hanbury-Brown and Twiss effect used to measure the size of stars?

I understand what an Hanbury Brown and Twiss (HBT) interferometer does, but how can this be used to measure the apparent angular diameter of some object? What is the mathematical explaination?
5
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3answers
812 views

Tensor product of Hilbert spaces and non-interacting particles

Consider a system of N quantum mechanical particles described on Hilbert spaces $\mathcal{H}_1,...,\mathcal{H}_N$ and with Hamiltonians $H_1,...,H_N$. The Hamiltonian operator $H_1$ acts on the ...
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1answer
140 views

How Is Entanglement Created Among Qubits?

How are qubits entangled? I understand the basics of entanglement but what I do not get is how it occurs in nature or in the lab. What causes entanglement to occur or what is done to the particle to ...
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1answer
380 views

Is the total energy of a quantum system the sum of the particle energies?

I really should know this off by heart (this is my field...) but I never really grasped the difference between the total wavefunction of a system and the wavefunctions of particles within it, so it ...
4
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2answers
242 views

Uniqueness of eigenvector representation in a complete set of compatible observables [duplicate]

Possible Duplicate: Uniqueness of eigenvector representation in a complete set of compatible observables Sakurai states that if we have a complete, maximal set of compatible observables, ...
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2answers
131 views

Space expansion effect on wavelengths across two points in space

Is the expansion of space taken into consideration when calculating light or any (Radio to Gamma) wave length distance and speed? I know C is a constant, but my concern is if "space expansion" is ...
5
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1answer
37 views

A question from Ticcati's red QFT textbook.

From Ticcati's textbook, he asks to show that from the axioms of position operator we get that: $$ \text{e}^{-ia\cdot P} |x\rangle = |x+a\rangle $$ where the axioms are: $$ X=X^{\dagger} $$ If ...
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1answer
450 views

electric dipole momentum calculation

I'm studying the linear electric susceptibility, using Schroedinger equation and perturbation theory of the interaction potential $$V=-\mu \cdot E$$ and the book arrive to an expression where ...
3
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2answers
410 views

Uniqueness of eigenvector representation in a complete set of compatible observables

Sakurai states that if we have a complete, maximal set of compatible observables, say $A,B,C...$ Then, an eigenvector represented by $|a,b,c....>$, where $a,b,c...$ are respective eigenvalues, is ...
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3answers
338 views

Testing my understanding of QM - The Double Slit Experiment without the slit

First off, sorry to throw in another question from someone who hasn't studied the maths. I'd like to see if I have a correct (if very basic and non-mathematical) understanding of the wave and ...
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4answers
554 views

How can I show that an arbitrary wavefunction in a 1D SHO is periodic in time?

I want to show that an arbitrary wavefunction $f$ in a one dimensional harmonic potential reproduces itself after a period T up to a phase factor: $f(x,t+T)=Af(x,t)$, $|A|=1$ I am not sure if this ...
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3answers
450 views

Heisenberg picture saves locality in QM?

David Deutsch recently released a paper titled "The vindication of locality" where he argues that by using the Heisenberg picture rather than the Schroedinger picture, you can "save" locality. The ...
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1answer
480 views

Question on ladder operators

Suppose we have a finite , discrete set of orthonormal states $|k\rangle $ We can construct raising and lowering operators intuitively, for example $$a_+ =\sum_{k=1}^nC_{k+1}|k+1\rangle \langle k|$$ ...
3
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1answer
741 views

Time-Dependent Potentials in Quantum Mechanics

A potential that depends on time is usually solved using the time dependent perturbation theory in standard undergraduate textbooks in quantum mechanics. The reason usually mentioned is that time ...
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4answers
305 views

Interaction of matter with EM fields

For the interaction between electromagnetic fields and matter, when do we have to include quantization of the EM field and when we can ignore it? when do we have to include quantization of atomic ...
6
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1answer
88 views

Optimality of the CHSH strategy

The maximum achievable probability of the Clauser-Horne-Shimony-Holt game is $\cos^2(\pi/8)\approx85.355\%,$ which can be proved with Tsirelson's inequality. But I don't imagine that this remained ...
6
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2answers
676 views

Decay from excited state to ground state

People frequently speak about an atomic system decaying from an excited state to the ground state. However, both the ground states and the excited states are defined as eigenstates of the Hamiltonian ...
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2answers
2k views

Rigorous justification for rotating wave approximation

Whenever I have encountered the rotating wave approximation, I have seen "the terms that we are neglecting correspond to rapid oscillations in the interaction Hamiltonian, so they will average to 0 in ...
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5answers
1k views

Is it possible to recover Classical Mechanics from Schrödinger's equation?

Let me explain in details. Let $\Psi=\Psi(x,t)$ be the wave function of a particle moving in a unidimensional space. Is there a way of writing $\Psi(x,t)$ so that $|\Psi(x,t)|^2$ represents the ...
0
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3answers
349 views

Has anyone theorized a connection between entropy and quantum uncertainty?

I apologize if this kind of idle theorizing is frowned upon here, but I was wondering if it is possible that the Second Law of Thermodynamics is a consequence of quantum uncertainty. I've heard ...
6
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2answers
592 views

Quantum Computing, Qubit Creation/Entanglement

I am currently a high school student researching quantum computing. I was referred to this site by Google and a friend. Currently I am researching the qubit part of quantum computing. My question is ...
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4answers
4k views

What is the physical sense of the transition dipole moment?

So if the states are the same we achieve the expectation value of the dipole moment for a given state. I mean $ \langle \mathbf{\mu} \rangle = \langle \psi \vert \hat{\mathbf{\mu}} \vert \psi ...
6
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1answer
292 views

Quantum systems with real structure

A lot has been said as to why quantum mechanics needs complex numbers. However, all measurements produce real values. Expectation values are real, the observables form a real Lie-algebra (use ...
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2answers
385 views

A proton is trapped in an infinitely deep well of L meters. The proton is in the first excited state. How does the excited state change the question.

The real question was: A proton is trapped in an infinitely deep well of 1*10^-14m. I suppose that is unimportant as that should only help us decided the limits of our integration. What I'm worried ...
2
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4answers
811 views

what is it called: box potential with one infinite wall

The finite square well and the infinite square well problem are well known, however is there a reason that there is almost no reference to the one sided infinite square well? Consider a particle ...
2
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0answers
101 views

How can one trace out polaritonic degrees of freedom?

I have read the paper "Steady state entanglement between hybrid light-matter qubits", arXiv:0711.1830v2. There, writers obtained density operator in matrix form after solving steady state equation ...
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2answers
403 views

Radar Frequency Bandwidth

I've come across an interesting question in the course of doing some exam review in a quantum mechanics book and thought I'd share it here. "What must be the frequency bandwidth of the detecting and ...
4
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2answers
756 views

Use of Operators in Quantum Mechanics

I understand the form of operators in use for quantum mechanics such as the momentum operator: $$\hat{\text{P}}=-ih\frac{d}{dx}$$ My question is in what ways can I use it and what am I getting back? ...
4
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1answer
71 views

Spekkens Toy Model, Internal Comonoids

I have been thinking about Spekkens Toy model in terms of interfaces. The Spekkens paper concerns a physics based on only being able to receive answers to half the number of questions necessary to ...
26
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8answers
2k views

Why $\displaystyle i\hbar\frac{\partial}{\partial t}$ can not be considered as the Hamiltonian operator?

In the time dependent Schrodinger equation $\displaystyle, H\Psi = i\hbar\frac{\partial}{\partial t}\Psi$ , the Hamiltonian operator is given by $\displaystyle H = -\frac{\hbar^2}{2m}\nabla^2+V$ ...
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1answer
97 views

Number of conditions for a two-particle state to be decomposable

Suppose we have a general two-particle state $ \Phi (x_1, x_2 ) = \sum_{n_1,n_2} \phi_{n_1,n_2}(x_1,x_2)|n_1,n_2> $, where $n_1$ can be any of $n$ possible states, and $n_2$ can be any of $m$ ...
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2answers
887 views

The mathematics of entanglement

I've finally managed to get a grasp on the Bell test experiments and all that they imply about our reality. Now I'm curious about the mathematical derivation which allowed Schrodinger to predict the ...
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2answers
190 views

Does a finite wave necessarily have to be non-monochromatic in reality?

Does a finite wave necessarily have to be non-monochromatic in reality, or is that implication just a result of the mathematical analysis? I always wonder at these sort of things that come out of a ...
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2answers
492 views

Has anyone actually “seen” entanglement?

I want to know if the following has been done experimentally; after the spin (or any other characteristic with a probability of 50%) of 2 entangled particles has been measured, we change the spin of ...