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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Can we “safely” assume that quantum computing systems will be finite-dimensional?

This is a common assumption in the study of quantum computation to assume that the quantum systems involved are finite-dimensional, since qubits lives in the two-dimensional Hilbert space. According ...
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3answers
5k views

Difference between spin-orbit coupling and LS coupling (Russell-Saunders)

I'm having some trouble understand what the difference is between these two. It seems as though there are kind of the same, but that spin-orbit coupling reduces to LS coupling under certain ...
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2answers
466 views

Clebsch-Gordan in Fock Space?

When adding the angular momenta of two particles, you use Clebsch-Gordan coefficients, which allow you, in fancy language, to decompose the tensor product of two irreducible representations of the ...
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0answers
281 views

Wave functions for 2D potential with spin interactions

So consider a 2D system with a circular potential and a spin-orbit interaction: $V(r) = V_0 \theta(r_0 - r) + c r_0 V_0 L_z S_z \delta(r-r_0)$ where $\theta$ is step function. So the operators $...
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1answer
242 views

Wave Function of Particle in Nuclear Reaction

I was thinking and came up with the question of what happens to the wave function of a particle that decays into energy, say a neutron in a nuclear reaction. I know that conservation of probability ...
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7answers
10k views

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 $\left|...
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1answer
409 views

Density matrix and irreducible tensor operators

I'm reading those lecture notes on atomic physics. Yesterday I posed a question on reducible tensors, and today I have a question on their relation to the density matrix. If there's any information ...
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1answer
163 views

Systems with different particle statistics

Is there a way to describe interactions between systems with particles of different species, that is to say with different statistics? For example: I am placing a boson next to a free fermion gas. ...
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2answers
1k views

Proving that $i\hbar\frac{\partial}{\partial \mathbf{p}}$ is the operator of $\mathbf{x}$ in momentum space

How can I prove that $i\hbar\frac{\partial}{\partial \mathbf{p}}$ is the operator of $\mathbf{x}$ in momentum space?
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0answers
166 views

Quantum Hamiltonian commuting with the Pauli-Runge vector

I have to prove that $[A_j, H] = 0$, with; $$\vec{A} = \frac{1}{2Ze^{2}m}(\vec{L} \times \vec{P} - \vec{p} \times \vec{L}) + \frac{\vec{r}}{r}$$ $$H = \frac{p^2}{2m} - \frac{Ze^2}{r}$$ And, $Z, e, m$...
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0answers
77 views

Is it possible to derive fermi-dirac or bose-einstein statistics using quantum operator formulations?

I've been looking through theory on identical particles to get a better grasp of the uncertainty principle but it would be very interesting if these results could be extracted from the formalism as ...
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1answer
801 views

Derivation of Matrix Components of Hamiltonian in Tight Binding Method

Im currently struggling with the description of the tight binding method in the original paper by Slater and Koster from 1954 (where a free version of the paper can be found under this link). In ...
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0answers
1k views

Differences between time-independent and time-dependent Schrödinger equation for potential generation

Suppose I wanted to develop a potential describing the interaction between two lithium atoms. One way to do this is to calculate the energy between the two lithium atoms for various distances and ...
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1answer
137 views

Operator that takes us from one density matrix to another?

Let's say we have two systems A and B. Each system is described by a density matrix $\rho_A$ and $\rho_B$. I'm wondering about the formal notation to write down the expectation value of an operator ...
3
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0answers
168 views

Fock Subspaces and Weight Vectors

This is my first time taking a physics course (I'm a mathematics major), so I'm encountering a lot of new things, which I'm kind of expected to know. In particular, how to work with Bosons. I've got ...
5
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3answers
391 views

Nobel Prize 2013: What is it about? [closed]

I would really like to understand Higgs-Englert’s discovery that earned them the 2013 physics Nobel prize. I tried reading their work, but understood nothing of it unfortunately. The reason why I’m ...
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0answers
65 views

Has advanced radiation been detected experimentally?

I would like to know whether there has been an experimental detection of advanced radiation. I seem to recall reading about such an experiment but I can't find any reference to it on the interwebs so ...
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2answers
327 views

How to understand wavefunction in quantum mechanics in math

I am reading some introduction on quantum mechanics. I don't understand all but I get the point that the wavefunction tells some probability aspects. In one book, they show one example of the ...
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1answer
4k views

How to find the wavefunction that solves an infinite square well with a delta function well in the middle?

Solutions for the wavefunction in an infinite square well with a delta function barrier in the middle are easily found online (see here for an example). I am wondering what the wavefunction is for an ...
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3answers
4k views

Why is it difficult to differentiate between interference and diffraction?

Why is it difficult to differentiate between interference and diffraction? Is it because we don't clearly understand how both of these phenomenon takes place? My thoughts: From an answer to one of ...
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5answers
2k views

Do orbitals overlap?

Yes, as the title states: Do orbitals overlap ? I mean, if I take a look at this figure... I see the distribution in different orbitals. So if for example I take the S orbitals, they are all just ...
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2answers
208 views

How does interaction of a system with the environment lead to the damping of interference terms?

A general way to describe a system $S$ that is entangled with an environment $E$ is $\rho_{S}=Tr(\rho_{SE})=\sum\limits_{m,n}c_mc^*_n |s_m\rangle \langle s_n| \langle e_n|e_m\rangle$ with $\psi_S=\...
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1answer
653 views

Quantum Mechanics and the Airy Function, the physics of the turning point

I'm working with the Airy function, and the book states at $x=0$ is a turning point, and there are two very different behaviors on either side. In general what a does a turning point mean in ...
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1answer
74 views

Can entanglement with an inaccessible system be useful?

Quantum phenomena in bipartite pure state systems like teleportation are pretty well understood. What I'm interested in is the following situation: Alice, Bob and Charlie hold some general tripartite ...
3
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1answer
773 views

Why is Quantum Teleportation important in Cryptography?

I think the physical principle is that (Wikipedia): For every qubit teleported, Alice needs to send Bob two classical bits of information. These two classical bits do not carry complete ...
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1answer
548 views

Quantum harmonic Oscillator analytic method

I'm using a book from Griffiths, I got really stuck about how he arrived at the approximate solution, is it just by trying( trial solution method?), I really appreciate any help on this. $$-\frac{\...
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1answer
264 views

How deep is the region near an event horizon where Hawking radiation is generated?

In other words, how strong does gravity have to be to cause Hawking radiation to occur?
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1answer
1k views

Momentum variance in momentum space for particle in a box

My assignment asks me to compute the momentum space wavefunction of the nth energy eigenstate of the particle in a one-dimensional infinite square well, then "show that your result is in agreement ...
3
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1answer
253 views

Superpositions with two observers

This is a bit of an odd question. I'm not a physicist, so bear with me if I say something wrong. Lets say you have some sort of quantum event where matter is in a superposition. Standing next to you ...
3
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1answer
611 views

Path Integral on a circle (calculation of phase and linear independance)

I am reading Schulman's "Techniques and applications of path integration" chapter on Path integrals on multiply-connected spaces. In the first section he calculates the path integral of a free ...
4
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4answers
654 views

Experimental evidence of Pauli's exclusion principle

A fermion is described by a set of quantum numbers, this set of numbers lead us to a unique wave function. If two fermions are described by the same wave function (violating the Pauli's exclusion ...
4
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1answer
249 views

Question on conserved quantities and Noether's theorem

I have a question about Noether's theorem in the context of QM, which I'll state in the context of the weak interaction but the basic point could be generalized. According to Noether's theorem, given ...
2
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0answers
474 views

QM Question about the Dirac Delta Potential

I just wrote down the solution for the bound state of the Dirac delta potential well, for $E<0$, and apparently there is only one specific energy for the bound state, and it is negative. I solved ...
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2answers
207 views

Why is it energetically favourable for molecular bonds to form from a QM point of view?

For example, if you have two hydrogen atoms and an oxygen atom, they are all electrically neutral and don't attract each other. But then if they manage to get "close enough" somehow they snap together ...
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1answer
462 views

Degeneracy in n-dimensional potential well

Knowing that degeneracy occurs in n-dimensional infinite potential well where two wave functions correspond to the same energy, can the same be said for the finite potential well?
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1answer
268 views

Classically, how can an electron orbiting a proton radiate given its relativistic energy

In classical relativistic Electrodynamics, we are often told that any accelerating point charge inherently radiates (Bremstrallung). (This is the basis for the need for a QM conception of electrons.) ...
2
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1answer
643 views

Given wave function at $t=0$, what is the process of deriving time dependent wave equation? [closed]

Suppose $$\Psi (x, t=0)=Ae^{i\alpha _1}\psi _1(x)+Be^{i\alpha _2}\psi_2(x)+Ce^{i\alpha _3}\psi_3(x).$$ If $\psi _n$ are the energy eigenfunctions how would I derive $\Psi (x,t)$? I am having trouble ...
2
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1answer
2k views

Overlap integral and probability

I have a question regarding how to extract probability from an overlap integral. Specifically, I am calculating the probability of a particle in a bound state in a delta potential $V=-\alpha \delta(x)$...
2
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0answers
46 views

What is a good target to aim for when teaching myself quantum mechanics? [duplicate]

I'm interested in teaching myself quantum mechanics, and I'm looking for a good goal to aim for. I've got an undergrad maths degree and a graduate degree in probability theory and stochastic ...
5
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2answers
422 views

Why does the Dopfer EPR experiment require coincidence counting?

Dopfer Momentum-EPR experiment (1998) seems to provide a interesting tweak in the EPR experiment. To read more details on this experiment, see: Page 3 (labelled S290) of 'Experiment and the ...
3
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1answer
100 views

Analytic expression for non-trivial commutators

Motivated by a previous question, consider bosonic creation/anihilation operators $a, a^+$ such that $[a, a^+]=1$, and $N = a^+a$. Is there an analytic expression for the following commutators: $[e^...
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2answers
249 views

Stern-Gerlach and Hund's second rule

According to Hund's second rule, the spin tends to be maximal. That would, in my understanding, imply that, regarding the Stern-Gerlach experiment, the important electron in a silver atom has spin 1/...
2
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0answers
97 views

Is everything in the universe discrete? [duplicate]

When beginning my education, I regarded nearly everything as continuous and analog in nature: Physical objects could have any mass on a continuous scale Light sources could emit any intensity of ...
1
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3answers
858 views

Simple Quantum Mechanics Question about The Commutator of Translation Operators

Say there is $\hat{J} = \exp[-i \hat{p} l/ \hbar]$ and $\hat{U}= \exp[-i\hat{H}t/ \hbar]$, where $\hat{H}$ is time-independent. Can we say anything about $[\hat{J},\hat{U}]$? Is it zero? How do we ...
4
votes
2answers
918 views

Normalization of the path integral

When one defines the path integral propagator, there is the need to normalize the propagator (since it would give you a probability density). There are two formulas which are used. 1) Original (v1+v2)...
3
votes
1answer
127 views

A change of sign in the electron-hole second quantization form

It is common to see people do a change of sign in the so called electron-hole representation, namely, $$ b^{\dagger}_{-k}=a_{v,k} $$ similar argument also seen in 1992 mattuck's book "guide to ...
3
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1answer
494 views

Minus Sign in Feynman Diagram

I've been reading these notes and I can't figure out the why on P.120, it is said that The fermionic statistics mean that the first diagram has an extra minus sign relative to the ψψ scattering ...
5
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1answer
461 views

Quantum tunneling effect in a potential of the kind $V(x)=A\frac{x^2}{1+x^4}$

Given a potential: $$V(x)=A\frac{x^2}{1+x^4}$$ with $A\gt 1$ and a quantum particle inside the well around the point $x=0$. I'm stuck on the calculation of the transmission and reflection coefficients ...
3
votes
1answer
688 views

Hubbard-Stratonovich transformation and mean-field approximation

For an interacting quantum system, Hubbard-Stratonovich transformation and mean-field field approximation are methods often used to decouple interaction terms in the Hamiltonian. In the first method, ...
4
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1answer
168 views

Entropy inequality

Assume that you have two bipartite systems $\rho_1^{AB},\rho_2^{AB}$ then I would like to prove the following: $$S(\frac{1}{2}( \rho_1^{AB}+I^A\otimes\rho_2^B))+S(\frac{1}{2}(\rho_2^{AB}+I^A\otimes\...