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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15 views

Creation and Annihilation operators… How to find?

I get so confused when trying to find this....please describe it as simply as possible but keep in mind I have no budget whatsoever to pay for textbooks, so here goes: How do you find the creation and ...
1
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0answers
23 views

Spectral lines and QM

In the various presentations I've seen so far in atomic physics of series such as the Balmer series, the wavelength of each spectral line is definite - but in QM, free particles have no definite ...
3
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4answers
176 views

Can we change a photon's frequency in mid-air?

Can we have a light source emitting photons in the infrared range and after, lets say, 5 meters, these photons become a photon in the x-ray range? The only way I know we can change a photon's ...
-2
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1answer
49 views

Are there nonlinear models of quantum mechanics which forbid superluminal signaling?

What would a nonlinear model of quantum mechanics which forbids superluminal signaling look like? Of course, a nonlinear $\psi$-ontic theory with entangled states could have superluminal effects upon ...
1
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0answers
17 views

Lindhard function for surface plasmon

Is there anybody that knows how to calculate the Lindhard function for the surface plasmon (between the surface of two metals of different dielectrics)? What I'm looking for is to find this function ...
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1answer
14 views

Particle on a ring model for electron motion in Porphine and highest occupied state

I'm studying for a test and I came across the following question: The particle on a ring is a useful model for the motion of electrons around the porphine ring. We may treat the group as a ...
2
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0answers
76 views

Why is imaginary time “outdated”? [on hold]

I was looking at reviews for Sakurai's Quantum Mechanics textbook, and some mentioned it being outdated, specifically mentioning his use of imaginary time. Is this something most people think? I can't ...
1
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1answer
24 views

How are energy states of photons reason for frequency independence in Compton scattering

I am reading on Compton scattering, more specifically on how Compton interpreted his results. He observed that the frequency of the scattered radiation was independent of the material used, so he ...
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0answers
27 views

Partial diagonalization of the Fock matrix

I'm currently writing my dissertation on the application of SCF semi-empirical methods to large systems, in particular proteins, and I'm stuck with a problem: I don't understand why, given the fact ...
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1answer
53 views

Interpretation of Fermi-Dirac statistics

I was reading that as temperature increases the energy at which $n(E)=0.5$ shifts to lower energies as these lower energy states become depopulated. Could someone explain that, what it means and why ...
1
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0answers
33 views

WKB Quantization Condition - negative?

In deriving the quantization condition for a bound state in a potential with "no verticle walls" we start with the WKB connection formulas to find the wavefunction in the interior of the well ...
0
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1answer
33 views

How much time between measurements do you have in order to make the same measurement on a particle?

As I understand it, you can make a measurement on a particle and if you quickly carry out a second measurement you will get the same outcome as the prior measurement. If this is the case, how much ...
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3answers
48 views

Energy of system in eigenstate of Hamiltonian

I know how to find the spectrum of the Hamiltonian to get the allowed energies for a system. If the spectrum is quantized, I can get definite values for each energy level. But when the system is in ...
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2answers
32 views

Allowed system energies from quantized Hamiltonian spectra

To find the allowed energies for a system, I can find the spectrum of the Hamiltonian $\hat{H}_{\psi}$ given a wavefunction $\psi$ representing the state of the system. 3 cases might happen: either ...
0
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1answer
40 views

Neutrino mass and the Majorana equation

I can't seem find this on the Internet. What does the Majorana equation predict neutrino masses to be (if they were their own antiparticle), and how? (I have little understanding of spinors, btw...) ...
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0answers
14 views

What are the conditions of wave function continuity when solving for Dirac Spinors as done in “Klein paradox” paper by Novoselov?

In the paper "Chiral tunneling and Klein paradox" paper by Katsnelson, Novoselov, and Geim, they use the wave function for Dirac spinors. What are the conditions for continuity of the wave function ...
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1answer
29 views

Why does negative energy imply that a system is bounded? [duplicate]

I wanted to know why "negative energy" of a two particle system implies that it is bounded. That is what happens in the case of a hydrogen atom; my textbooks say so, but they do not give any reason ...
0
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1answer
31 views

Physically realizable (quantum) system

Given a system of arbitrary number of commuting observables, can one always exhibit a system that realizes it? For example, suppose we have 3 diagonal (and, therefore, commuting) matrices $X= \left( ...
1
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2answers
20 views

Notions of “confined” and “metastable” states?

What is the exact definition of terms "confined state" and "metastable state", in the context of quantum mechanics? Can we also have a "confined metastable state"? Can we somehow easily link these ...
1
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3answers
68 views

Tensor product in quantum mechanics

In Cohen-Tannoudji's Quantum Mechanics book the tensor product of two two Hilbert spaces $(\mathcal H = \mathcal H_1 \otimes \mathcal H_2)$ was introduced in (2.312) by saying that to every pair of ...
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0answers
33 views

How do we know $\psi$ depends on $n,l,m$ [on hold]

Regarding the separation of $\psi$ to an angular and radial part, why does each part have a specific dependence of the quantum numbers? How can Schrodinger equation describe a system just from its ...
0
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0answers
28 views

Identity for the product of propagators

Working in 1 spacial dimension, it has been written that $$\begin{align} \int K(x_f,x,t_2)K(x,x_0,t_1)dx &= \int \langle x_f|e^{-\frac{i}{\hbar}\hat{H}t_2}|x\rangle \langle ...
0
votes
1answer
40 views

Time reversal on superposition: I think [duplicate]

Imagine I have a box, and in it, I have a photon in a superposition of state |1> and |0>. I look into the box and register that the photon is in state |1>. Now, if I have ALL information in the ...
1
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1answer
34 views

Solving for the density operator in the quantum Brownian motion master equation

I want to solve for the density operator in the quantum Brownian motion master equation, \begin{align} \begin{aligned} ...
1
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1answer
76 views

Hartree Fock equations

I don't understand how the Hartree Fock equations define an iterative method! For this discussion, I am referring to the HF equations as described here: click me! Basically if you guess a bunch of ...
1
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1answer
33 views

Permutation operator and second quantization

I just read that a permutation operator $P_{i,j}$ acts on a product state $|a_1,...,a_n \rangle \in H^n$ by $$P_{i,j} |a_1,...,a_i,a_j,...a_n\rangle = |a_1,...,a_j,a_i,...a_n \rangle .$$ Now my ...
6
votes
2answers
82 views

Triangular barrier in infinite potential well

Suppose I am looking to solve the wavefunction for the following 1D potential: $$U(x) = \begin{cases}V_0\frac{a-|x|}{a}&\quad\text{for}\quad|x|<a ...
0
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0answers
38 views

How is tunneling probability? [on hold]

Let's say we have an alpha particle tunneling through a barrier of width 2 fm and height 30 MeV, and the alpha particle has an energy 1 MeV below that of the barrier. The tunneling probability is ...
-2
votes
1answer
31 views

Probability with expectational value [on hold]

How can I calculate: $$P(T)=T^2 b^2 |<n| \delta (x) |n>|^2~?$$ Where $P$ is the probability.
-1
votes
1answer
33 views

Expectation value of operators in quantum mechanics

Can the expectation value of an operator be zero?
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2answers
38 views

Show that a function takes the following form using the definition for the function of an operator

If $f(z)$ is a function with a Taylor series expansion $$f(z)=\sum _{ n=0 }^{ \infty }{c_n z^n },$$ then we define $$f(M)=\sum _{ n=0 }^{ \infty }{c_n M^n }.$$ First consider ...
6
votes
1answer
317 views

Have they really photographed light behaving both as a particle and a wave?

I just came across this article where they are claiming that they have photographed light behaving both as a wave and a particle! The paper has been published in Nature Communications and I read the ...
0
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1answer
21 views

Fine Structure Correction

The fine structure correction is composed of the relativistic correction and spin-orbit coupling. The lowest-order relativistic correction to the Hamiltonian is $$ H_r' = -\frac{p^4}{8m^3c^2}$$ ...
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0answers
38 views

Solving Schrodinger Equation with Anisotropic Effective Mass

How can I discretize a time-independent Schrodinger equation using the mass tensor and considering the valley degeneracy for the specific material at hand? I intend to investigate the confinement ...
1
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1answer
33 views

Why does the nuclear volume scale (roughly) linearly with number of nucleons?

As far as I know, it is the fermi repulsion that gives a collection of protons or neutrons its finite size. But this only acts on indistinguishable fermions. If the protons and neutrons do not repel ...
0
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2answers
48 views

The delta function as an eigenfunction of the position operator explanation

$\delta (\textbf{r})$ can be interpreted as a wavefunction. [...] It is non-vanishing only for $\textbf{r}=0$. [...] $\delta(\textbf{r})$ is an eigenfunction of the position operator with ...
-2
votes
1answer
40 views

Perturbation theory of states [on hold]

A particle in 1 dimension with mass $m$ is in potential well with $V = 0$ for $–a/2 < x < a/2$ and infinite potential elsewhere. The particle is initially in the state $n = 10^9 + 1$, with the ...
3
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0answers
130 views

What concepts could I teach to children in a game about quantum-mechanics? [on hold]

I think that games can also be used to teach things to young people or childs, different than for example a book and could be more "direct" than teaching them all the math background, I would like to ...
-3
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0answers
22 views

What is the best materiels for fixed target experiments with a linear particle accelerator? [on hold]

I need the best materiel for fixed target experiments using linear particle accelerators when accelerating electrons. By "best" I mean one that when the accelerated electron beam collides with it the ...
-1
votes
1answer
28 views

Calculating values related to angular momentum and then their uncertainties [on hold]

Here is the problem: And here is my work (sorry it is handwritten, it would take a while to type this out) My problem is that I'm not sure if it's right or if it makes sense to keep getting 0 ...
0
votes
2answers
50 views

Normalization of wave function meaning…?

I just have one question. I'm doing a problem where I'm told to normalize a wave function, which is split up into two regions, namely where $r \leq r_0$ and $r > r_0$. My question is, why am I ...
2
votes
0answers
30 views

How to solve a difficult equation describing large vacuum fluctuations?

Suppose that a Quantum System can be described by the wavefunction $\psi(\vec{x},t)$, but due to the occurence of chaotic noise within the Quantum System, only the "filtered" wavefunction ...
1
vote
1answer
85 views

Can I state that $\Psi (x_1, \dots , x_n,t)= \sum_{i=1}^n a_i \psi (x_i,t) $ via superposition?

Given that the hamiltonian $\hat H$ of a system is a linear operator and $\dot \psi (x_i,t)$ does not depend on spatial coordinates $x_1, ..., x_n$ with bases $\hat e_1, ... , \hat e_n$ can I state ...
0
votes
0answers
62 views

Quantum mechanical expectation of angular momentum along different axes [on hold]

This is a question from Concepts of Quantum Mechanics by Mathur & Singh, and I don't know where I should start from: Show that, for a state $|j,m \rangle$, corresponding to a definite value of ...
-4
votes
1answer
17 views

Uncertainty of energy for harmonic oscillator at ground state and first excited state

How does one calculate the energy uncertainty of the harmonic oscillator in the ground state and first excited state?
0
votes
1answer
75 views

How does one normalize this wavefunction? [on hold]

Here is the question: So I could write $ N = \dfrac{1}{{\sqrt{<Ψ|Ψ>}}} $, right? Considering the parentheses in the exponential term, it looks like a good idea to switch to spherical polar ...
-5
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0answers
60 views

Can I have superposition equation? [on hold]

I would like superposition equation. I learn functions, boundaries of strings, boundaries of functions, differential equations, derivatives and integrals to understand superpositions from Mathematical ...
2
votes
1answer
30 views

Non-degenerate or degenerate perturbation theory for a non-degenerate level of a system with other levels degenerate?

To decide whether I have to use non-degenerate or degenerate perturbation theory, I have to look only on whether the energy level I am calculating corrections to is degenerate, the degree of ...
0
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0answers
28 views

How to derive De Haas–van Alphen effect?

I was reading Solid State Physics by Kittel and they manage to derive De Haas–van Alphen effect by invoking the Bohr-Sommerfeld model. This feels unsatisfactory to me. Can someone derive this using ...
3
votes
0answers
71 views

How to check whether Schrödinger's cat was in superposition of states?

Suppose we can make an arbitrarily precise preparation of a Schrödinger's cat (and isolate it arbitrarily well so that decoherence is not a problem). If we prepare lots of cats in this state, what ...