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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32 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf ...
4
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0answers
47 views

Why doesn't Fermi's golden rule distinguish attraction from repulsion?

Let's say I have two distinguishable charged particles interacting electrostatically. In Fermi's golden rule, the two particles can change state at a rate proportional to: $$|\langle \psi_f | H_{int} ...
2
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1answer
44 views

Free particle Schrödinger Equation

Some sources give the free-particle solution to Schrödinger equation as $$\psi(x,t) =Ae^{i(kx-\omega t)} + Be^{-i(kx+\omega t)}$$ while some sources give it as $$\psi(x,t) =Ae^{i(kx-\omega t)}$$ ...
2
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0answers
43 views

Physical consequences of non-trivial quantum states homology

The set of quantum states of a finite dimensional system is a complex projective space, whose homology groups are non-trivial http://en.wikipedia.org/wiki/Complex_projective_space#Homology. Has this ...
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2answers
73 views

Uncertainty principle in Quantum mechanics

The Uncertainty principle says that "△x△p>h/2"; we cannot precisely obtain both position $x$ and momentum $p$ simultaneously. Is this because the uncertainty is the natural characteristic or it is ...
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2answers
58 views

Free-particle solution to Schrödinger Equation

The free particle solution in stationary state (with definite energy) to the Schrödinger equation is $$\psi(x,t) =Ae^{i(kx-\omega t)} + Be^{-i(kx+\omega t)}$$ Since the energy is definite, and ...
9
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5answers
349 views

What happens when we bring an electron and a proton together?

I have a couple of conceptual questions that I have always been asking myself. Suppose we have an electron and a proton at very large distance apart, with nothing in their way. They would feel each ...
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1answer
25 views

Do I need to take both particles' momentum into account in photoelectric emission? [closed]

An aluminum dust particle of mass $m=2.2*10^{-18}$ grams is floating in space ( initial velocity is zero). The particle emits electron under influence of a photon whose frequency is $8*10^{17}$ ...
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0answers
38 views

Showing that the maximum possible uncertainty for any observable is half the difference between its maximum and minimum eigenvalues

Show that the maximum possible uncertainty for any observable is $\frac{1}{2}|x_2 - x_1|$ where $x_1$ and $x_2$ are the extreme eigenvalues of X (Maximize $\Sigma_i p_ix_i^2 - (\Sigma_i p_ix_i)^2$) ...
3
votes
1answer
243 views

Why do we must initially assume that the wavefunction is complex?

The sound waves are real, and they can interfere, so corresponding apparat may be used in quantum mechanics. We also may use the time dependence in a form of orthogonal matrix multiplying the initial ...
1
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1answer
91 views

Free particle propagator - Evaluating Integral

In path integral formalism, when evaluating the free particle propagator, we obtain the functional integral of the form, $$ K_0 = \lim_{n\rightarrow\infty} \bigg( \frac{m}{2\pi ...
0
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0answers
43 views

Completeness of the state space and Hilbert space [duplicate]

I am wondering just why is it supposed that quantum states lie in a Hilbert space, which mathematically requires completeness? In other words, what does completeness (defined in terms of Cauchy ...
8
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2answers
444 views

What is probability current in quantum mechanics?

What is probability current in quantum mechanics? Why define such a thing? I mean the meaning of probability current. I know the formula for it but I just don't get the idea of a flow of probability ...
4
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4answers
367 views

Perturbative Quantum Mechanics

I am, in full generality, confused about perturbation theory in quantum mechanics. My textbook and Wikipedia have the same general approach to explaining it: given some Hamiltonian $H=H^{(0)} + ...
0
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3answers
55 views

Why the distance between peaks of the probability distribution function decreases when n increases?

In the solution of Schrödinger Equation for harmonic oscillator why the distance between peaks of the probability distribution function decreases when n increases? Is there a good reason for it or is ...
5
votes
1answer
118 views
+50

Addition of spin angular momentum for massless particles

How do I add the spin angular momentum of massless particles, like photons, where only the transverse polarizations are allowed? If all three polarizations were allowed, this would be an easy ...
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0answers
65 views

Momentum and position operators in Schrödinger representation

I was going through some intro notes on path integral (for QFT), and am stuck with this equation for position and momentum in Schrödinger (position) representation, $$ \hat{1} =\int ...
2
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0answers
74 views

How symmetry is related to the degeneracy?

I have several questions about symmetry in quantum mechanics. It is often said that the degeneracy is the dimension of irreducible representation. I can understand that if the Hamiltonian has a ...
0
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0answers
28 views

band gaps in tight binding model

What happens at the zone boundaries of the brillouin zones in the tight binding model? How does the band gap originate in the TB model?
2
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0answers
39 views

Is there any connection between “Lagrangian and Eulerian formalism of fluid” and “Heisenberg and Shrodinger picture”

Is there any connection between "Lagrangian and Eulerian formalism of fluid" and "Heisenberg and Shrodinger picture of Quantum mechanics"? Thanks!
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0answers
59 views

Does nonlocal theory violate causality?

Let's talk about two kinds of nonlocal theories. The first one frequently derives from integrating out part of the degrees of freedom to obtain a kind of effective theory. Probably, we get an integral ...
2
votes
1answer
45 views

Solving the 1-d time-independent Schroedinger's equation with an infinite boundary

In my introductory modern physics class we have examined time-independent solutions to the Schrödinger equation in 1 dimension. We looked at a few cases without finite boundary, e.g., free particles ...
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0answers
46 views

Sudden Approximation for Beta Decay of Tritium Atom

I am working out this problem right now, and I'm confused by the answers I'm getting. Problem: A tritium nucleus (Z = 1) in a tritium atom undergoes beta decay, i.e., a neutron in the nucleus emits an ...
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0answers
71 views

Could the phase factor $i$ be replaced by “matrix representation” totally in quantum mechanics? [duplicate]

It seems that $i$ plays an important role in quantum mechanics (Q.M.). On the other hand, linear algebra plays such an important role in Q.M. too. So would linear algebra, such as a matrix be able to ...
2
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0answers
53 views

Electromagnetic force interaction

As far as I know, the electromagnetic force only interacts on particles with electrical charge, but I was told that the electromagnetic force was involved in the following reaction: ...
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0answers
19 views

A question about Gell-Mann Low theorem?

Let $|\Psi_0\rangle$ be an eigenstate of $H_0$ with energy $E_0$ and let the 'interacting' Hamiltonian be $H=H_0 + gV$, where $g$ is a coupling constant and $V$ the interaction term. We define a ...
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0answers
88 views

A few questions about interacting quantum field?

In interacting quantum field, we think that interaction is adiabatic switch on/off. So in the infinite past, we can think there is no interaction, so we can have particle interpretion. There are four ...
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0answers
37 views

Quantum fluctuations in the non-relativistic limit

Is there any way to describe quantum fluctuations in ordinary quantum mechanics? For instance, a proton fluctuating into a proton-$\pi^0$ state and then back to a proton? What are the relevant ...
6
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2answers
135 views

The gauge covariant derivative and it's substitution

I was wondering wether it would make a difference (in general) if I were to were introduce the gauge covariant derivative $$D_\mu=\partial_\mu+ieA_\mu$$ In the Lagrangian density and then derive the ...
0
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0answers
29 views

Solve Eigenvalues for Particles enclosed in a hard surface?

Is there a way to calculate the energy eigenvalues for a particle enclosed in an impenetrable enclosing surface? I tried evaluating the Fourier transformation of the Laplacian operator \begin{align} ...
3
votes
1answer
152 views

Why have $n$, $\ell$, $m_\ell$, $m_s$ been picked as quantum number symbols *in this order*?

I’m learning about electron configurations and don’t quite understand why $n$, $\ell$, $m_\ell$, $m_s$ have been picked as symbols for the quantum numbers. As far as I understand it, the principal ...
0
votes
2answers
40 views

Total energy of a quantum gas

I'm dealing with a quantum gas, thought as a system of N non-interacting particles. I would be tempted to say that the total energy of the system equals the sum of the energies of the single ...
2
votes
2answers
113 views

electron in the nucleus

In the event that the electron is in nucleus of the atom (via tunneling effects and other things I don't understand), How does QED deal with this situation?
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0answers
17 views

Average value of consecutive measurements of two observables

Suppose we had two boxes named "1" and "2", and suppose we can measure observables $A_1$ and $A_2$ from these boxes, respectively. $A_1$ and $A_2$ commute, meaning we can find a basis of simultaneous ...
2
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2answers
106 views

Expectation Value of a Dynamical Variable

In quantum mechanics, we generally take about "expectation values of dynamical variables". However, by the postulates of quantum mechanics, every dynamical variable in quantum theory is represented by ...
2
votes
1answer
64 views

Proving a step in this field-theoretic derivation of the Bogoliubov de Gennes (BdG) equations

In derivation of the BdG mean field Hamiltonian as follows, I have a confusion here in the second step: $H_{MF-eff} = \int ...
0
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0answers
23 views

Would superluminal signalling imply the violation of the No Cloning Theorem and unitarity?

The no-cloning theorem implies that we cannot use entanglement to send signals faster-than-light. Has anyone proved the contrapositive? That is, if we are given a system for superluminal signalling ...
0
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0answers
42 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 ...
1
vote
3answers
55 views

Help understanding proof in simultaneous diagonalization

The proof is from Principles of Quantum Mechanics by Shankar. The theorem is: If $\Omega$ and $\Lambda$ are two commuting Hermitian operators, there exists (at least) a basis of common eigenvectors ...
4
votes
1answer
78 views

What exactly does Aaron D. O'Connell's experiment show?

I watched a TED talk by the scientist Aaron D. O'Connell about actually seeing quantum superposition. The link to the talk is :- ...
2
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0answers
43 views

Spatial profile for a superconducting qubit's wavefunction

What is a spatial profile for a wavefunction of a superconducting qubit (such as say a flux qubit, charge qubit, or a transmon)? I am trying to calculate the energy shift of an superconducting qubit ...
1
vote
2answers
77 views

When combining three spin $\frac{1}{2}$ particles what are the corresponding states?

I want to combine three spin half particles and this is what I have so far. I used the lowering operator $J_{-}$ on the top states and found the following states fine: ...
0
votes
0answers
36 views

Angular momentum of 2d harmonic oscillator

So, I have the problem of determining the spectrum of H and L, in terms of creation and annihilation operators of angular momentum... The problem goes along with what is happening on this page. ...
4
votes
1answer
80 views

Symmetry and Degeneracy of Free Particles

Consider the hamiltonian $H=\frac{p_x^2}{2m}$ in 1-D. It is invariant under $p_x \rightarrow -p_x$. Again, this hamiltonian also has translational symmetry. Which one of these two is responsible for ...
2
votes
0answers
24 views

What is weak coupling of photon polarization to a pointer?

This question is refered to those who are familiar with the concept of weak measurement. In short: How can the polarization of a photon be coupled to the position of a pointer state? What is the ...
3
votes
1answer
76 views

Quantum mechanics and atomic bonding

I'm learning quantum mechanics in high school this year, and I have several doubts. I've done my research on various websites but my understanding is still fuzzy. I understand that when I punch a wall ...
2
votes
2answers
141 views

Does quantum randomness predicate an infinite number of realities?

I am a layman when it comes to physics and especially quantum mechanics. I have seen many documentaries on the subject, and often in these productions there is a physicist featured explaining the ...
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0answers
39 views

Simpler quantum “paradox” implying supraluminal connection

Executive summary: "Collapse of the wave function" is inherently supraluminal. I suggest an easier thought experiment to demonstrate the apparently supraluminal (or FTL) aspect of a quantum ...
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0answers
30 views

A small contradiction between periodic boundary condition and first Brilliouin zone

In condensed matter, one usually considers Bloch states inside the first Brilliouin zone, which, for 1d system with lattice constant $a$, is $-\pi/a<k<\pi/a$. But the basis of this, Bloch ...
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0answers
19 views

Uncertainty principle characterizing metallic bonding?

So I was trying to think through the statement that the uncertainty principle can characterize metallic bonding. I know that the uncertainty principle is: $\Delta p \Delta x = \frac{\hbar}{2}$. And ...