Tagged Questions

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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27 views

Any truly beautiful reading about quantum mechanics to beef up in sight of my final on the 27th? [duplicate]

I'm looking for good books to give me some more "taste" on beautiful aspects of QM. I'm actually studying for my undergraduate exam on the 27th november that comes in a strong academic flavour and ...
0
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0answers
25 views

Quantization in a 2D quasicrystal?

let be the Schroedinger equation with a potential in a quascristal $$ -( \partial _{x}^{2}+ \partial _{y}^{2}) \Psi (x,y)+ V(x,y)=E_{n} \Psi (x,y) $$ if we were in a crystal we could impose the ...
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1answer
38 views

Integral over scalar product of eigenfunction of momentum operator and harmonic oscillator one

Recently I've met following expression: $$ \tag 2 \sum_{n}f(n)\int dp~ |\langle p | n\rangle|^{2} = 2\pi \sum_{n}f(n). $$ Here $|n>$ is eigenfunction of harmonic oscillator with energy $$E_{n} = ...
2
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0answers
37 views

On the Equivalence of Schrodinger and Heisenberg Descriptions of Quantum Mechanics and Observability

I'm not a physicist, but rather a control (feedback) systems engineer eager to understand more than just a cursory explanation of quantum mechanics. The StackExchange has been an excellent forum for ...
1
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1answer
50 views

How does current flow in superconductors if Cooper pairs have zero momentum?

I've been reading a lot of condensed matter textbooks, which state both that the net momentum of a Cooper pair in a superconductor is zero, and that Cooper pairs have momentum when they carry current. ...
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1answer
60 views

Commutation relation of position and momentum using Dirac notation

This is likely a very trivial/silly question, but in following a derivation of the position and momentum commutation relation using the dirac notation, I am having trouble justifying a certain step. ...
1
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3answers
146 views

Why does the Copenhagen interpretation assert randomness if this cannot be tested?

Why does the Copenhagen interpretation of QM assert that random events occur if such a claim cannot ever be proven or disproven? A related question: How to tell if QM is really random? Edit On ...
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0answers
48 views

Hardy's paradox (see the article “Quantum Mechanics, Local Realistic Theories, and Lorentz-Invariant Realistic Theories”)

Does this thought-experiment (Phys. Rev. Lett., Vol. 68, No. 20, page 2981, year 1992) represent a proof against Bohm's interpretation of the quantum mechanics? The analysis of Hardy rules out local ...
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0answers
19 views

intervalley optical phonon scattering

Is there any difference between intravalley and intervalley optical phonon scattering self-energies in NEGF method?(except that electron-phonon coupling constants)
1
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1answer
56 views

What really generates time evolution?

A fundamental principle of quantum mechanics, as far as I can tell, states that the Hamiltonian generates time evolution. A common result about generators are the following: let $\mathrm T$ be the ...
3
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2answers
77 views

Landau level degeneracy in symmetry gauge, finite system

As we know, Landau level degeneracy in a finite rectangular system is $\Phi/\Phi_0$, where $\Phi=BS$ is the total magnetic flux and $\Phi_0=h/q$ is the flux quanta. This can be easily derived using ...
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0answers
19 views

Bose Enhancement Factor

How may one explain the fact that the probability of a boson transferring to a state with an occupation number n is 'enhanced' by a factor of (1+n), compared to the classical case? (In the classical ...
0
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0answers
28 views

Hartree Fock exchange kernel

I would like to understand, how we calculate the exchange kernel of the Hartree Fock equations for a coulomb potential. So in slide 19 here for example you see the result, but I have not the ...
5
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4answers
128 views

Difference between kets $\left| -x\right\rangle$ and $-\left |x\right\rangle$?

While using dirac bra-ket notation for quantum mechanics, what's the difference if the minus sign is inside or outside the ket ? I know that $\left| -x\right\rangle$ and $- \left|x \right\rangle$ ...
14
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5answers
206 views

How is anything *not* ultimately a position measurement?

Consider measuring the momentum of an electron. You pass it through some kind of electromagnetic field, it strikes a photodetector (e.g. a CCD), and you back-calculate out the momentum of the ...
2
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3answers
138 views

What is the physical intuition behind the fact that 'energy is not continuous'?

First of all I am a novice regarding my knowledge of quantum mechanics. But curiously I do want to know what is the problem if energy is continuous like spontaneously flowing tap water. In fact I ...
4
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0answers
66 views

References to Mechanics (Classical, Quantum, Statistical) using Time-Scale calculus?

Time-Scale Calculus, is a theory which unifies ordinary (plus fractional and q-) calculus with discrete (and finite differences) calculus. In a sense, in a similar way the Lebesgue integral (or ...
0
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2answers
70 views

Indistinguishable particles and probability density

I am given the following (probably simple) exercise, but I think I misunderstand something: Let $\psi_{a,b}(r_1,r_2)$ be a two-particle state, calculate the probability density for distinguishable ...
3
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3answers
509 views

Wavefunction, probability and impossible events

A friend of mine asked me a question, which I considered trivial at first, but after a while gave rise to some doubts. For instance, we have a potential well in 1 dimension defined by $$ V(x)= ...
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0answers
51 views

How can we prove the commutator $[F(a^{\dagger}a),a^{\dagger}a]=0$

The spin operators defined by the Holstein-Primakoff transformation are $$ S^{+}=\hbar \sqrt{2S}a^{\dagger}\sqrt{1-\frac{a^{\dagger}a}{2S}} \\\ S^{-}=\hbar \sqrt{2S}\sqrt{1-\frac{a^{\dagger}a}{2S}}a ...
0
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0answers
21 views

Electron transmission in Landauer formalism: why just imaginary part?

In Landauer formalism the electron transmission function is defined as $T = Tr(G_M^\dagger\Gamma_LG_M\Gamma_R)$ where $G$ are Green's function of subsystems, index $L$ and $R$ means subsystem of ...
0
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1answer
28 views

Why is the unitary matrix relating the gamma matrices and their complex conjugates antisymmetical?

In Messiah's Quantum Mechanics Vol. II, properties of the Dirac matrices are derived. There is so-called fundamental theorem, which states that, Let $\gamma^\mu$ and $\gamma^{'\mu}$ be two systems of ...
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3answers
95 views

Can excited electrons fall back to their ground state without the emission of photons?

In gas discharge lamps, for example, a current composed of ionized atoms excites the electrons of the atoms of the gas, and when they fall back to their ground state photons are emitted. Why is the ...
4
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2answers
253 views

Do the probability density and the probability current density have a unit

I could not find what is the probability density and the probability current density of one-dimensional Schrödinger equation units?
3
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1answer
43 views

Is there a lower bound on energy needed to transfer one bit of information?

Let's say we want to transmit information between to stations (points in space). Is there a minimal energy required to transfer a single bit of information, assuming that we tolerate that the bit ...
4
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2answers
61 views

Partition function containing QM?

I am wondering about the partition function of the classical microcanonical ensemble. It contains Planck's constant and also an indistinguishability argument about the particles I am looking at and I ...
1
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1answer
54 views

What do position and momentum representations represent in QM?

In QFT we classify field operators according to how they transform under a given symmetry, i.e. in their being a basis for some representation of the symmetry group of the Hamiltonian/Lagrangian. This ...
1
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2answers
91 views

Do electrons “check in” at the quantized energy radius before they leap?

Quantum jumps inside atoms always have the same energy, at least in a hydrogen atom when jumping from $n=1$ to $n=2$, like from a 1s1 to a 2s1 state. My question is, if an electron can be anywhere in ...
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0answers
17 views

Quantum camera using euclidean rotation and kabbalah

I've been playing around with procedurally generated images and the kabbalah/tesseract the last few weeks. Imagine a 3D cube sitting on top of a 2D colour wheel. One thing I noticed is that 3D ...
0
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2answers
50 views

Expectation value expression Quantum Mechanics

Whilst working on a project I kept stumbeling across two different expressions for the standard deviation $\Delta{X}^2 = <(X - <X>)^2 >$ and the other $\Delta{X}^2 = <X^2> - ...
1
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2answers
46 views

How does EM heating cause motion?

Similar to how does heating cause motion, I'm trying to understand how a photon imparts motion to an atom, i.e. adds heat to a gas. I'm going to hazard a guess, and suggest this occurs something ...
1
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2answers
74 views

Energy-Time Uncertainty Principle and Photons

Heisenberg's uncertainty principle states that: $$ \Delta E \cdot \Delta t \ge \frac{\hbar}{2} $$ It is clear that this has nothing to do with the accuracy of our measurements, but rather is a ...
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3answers
103 views

Schrödinger equation derivation and Diffusion equation

I am aware of the debate on whether Schrödinger equation was derived or motivated. However, I have not seen this one that I describe below. Wonder if it could be relevant. If not historically but for ...
2
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1answer
111 views

What obstacles does de Broglie's pilot theory have to overcome? [duplicate]

I have been reading through a Wired article on pilot wave theory which talks about new evidence in support of Louis de Broglie's concept of pilot theory through experiments showing that the droplet in ...
4
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4answers
185 views

How big is an excited hydrogen atom?

Suppose an empty universe with the exception of a single hydrogen atom (1 proton, 1 electron). The electron may be in its ground state or it may be excited a certain number of levels. Suppose it is at ...
3
votes
1answer
139 views

Susy QM and Atiyah-Singer index theorem

Consider maps $t\mapsto x^i(t)$ from circle to some Riemannian (spin) manifold and lagrangian $$ \mathcal L = \frac12 g_{ij}(x) \partial_t x^i \partial_t x^j + \frac12 g_{ij} \psi^j \left(\delta^i_k ...
4
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2answers
82 views

How exactly does applying the Equipartition Theorem to radiation leads to UV catastrophe?

I'm reading a book by George Gamow, "Thirty years that shook Physics" and have trouble understanding his way of describing the UV catastrophe. In a first part he points out that applying the ...
1
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1answer
74 views

Difficulties in understanding basic energy equation in quantum mechanics [duplicate]

While reading a text book about basics of Quantum Mechanics, I came across a situation in which it is said that $E=\hbar\omega$ and also $E = \frac12mv^2=p^2/2m$ where $h$ Planck's constant ...
2
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0answers
51 views

Statistics of many body systems in pure states

My understanding of describing a system in thermal equilibrium is that we introduce an ideal thermal reservoir for convenience and then imagine that the system+reservoir samples all states of constant ...
1
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0answers
20 views

Fluctuation-dissipation in a quantum Ising Model

For the classical Ising model, the fluctuation-dissipation theorem tells us that the Magnetic susceptibility is proportional to the variance of the magnetization. Is there an equivalent relation for ...
0
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1answer
16 views

post selection and instantaneous communication [duplicate]

Does post selection lead to instantaneous communication between two points in space? Below is the scenario: Take two entangled qubits A and B. Seperate them out in space. Post select on qubit A to be ...
2
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0answers
79 views

Symmetry, gauge, and projective symmetry group (PSG)?

My following questions come from the understanding of the relations between the PSGs for two gauge-equivalent mean-field (MF) Hamiltonians (or MF ansatz). Considering the Schwinger-fermion ...
0
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2answers
55 views

If we were to hold a single atom in our hand, would it feel solid? [closed]

If we were to hold a single atom in our hand, would it feel solid? In addition, do all the matter that we feel solid actually a wave of probability? I'm not a physicist anyway.
2
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0answers
34 views

Tunneling from Dirac material into Schrodinger material?

When a Dirac material, like graphene or TI, has a connection with a normal metal which Schrodinger equation govern on their carriers, how could we manipulate the tunneling of electron from Dirac side ...
0
votes
1answer
53 views

What is the time dependent expectation value for momentum

For an electron in an equal linear superposition of two eigenstates in a one-dimensional infinitely deep square potential well of width L, how do you isolate the time dependent part of the expectation ...
0
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1answer
59 views

Working towards finding Clebsch-Gordan coefficients for a single electron

I'm really confused about a problem involving a single electron which eventually wants me to calculate Clebsch-Gordan coefficients. I think this is probably because, I've only ever seen examples done ...
1
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0answers
25 views

Why isn't there a different phase after fourier transformation in two lattices

I am trying to understand some solutions for graphenes energy dispersion. While most of it is clear, I don't get one step, when changing into k-space. Consindering two sublattices A and B with ...
0
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0answers
20 views

Screened potential of charged impurity in a 2-dimentional electron gas

What's the analytical relation of screened potential of charged impurity in a 2-dimentional electron gas?
2
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1answer
58 views

Unitarity and measurement

I used to believed that the wavefunction collapse came from the interaction of the system we want to measure {S} with the measurement apparatus {M} : {S} undergoing a non unitary transformation, but ...
3
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2answers
79 views

Confusion with rotation operator definition in Shankar

In Shankar quantum mechanics on page 306-307 it has the following: 12.2. Rotations in Two Dimensions Classically, the effect of a rotation $\phi_0\mathbf{k}$, i.e., by an angle $\phi_0$ about ...