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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2answers
98 views

Why do objects have size? [closed]

What is the reason objects, like coffee mugs, have size?
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2answers
204 views

Why are the spin operators defined as they are?

$$\begin{align*}S_z &= \frac{\hbar}{2} \left(\left|+\right>\left<+\right| - \left|-\right>\left<-\right|\right)\\ S_y &= i\frac{\hbar}{2} \left(\left|-\right>\left<+\right| - ...
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3answers
315 views

Is there a prediction of quantum mechanics that could be construed as representing an “energy-time uncertainty relation?” [duplicate]

As the title suggests. Is there a prediction of quantum mechanics that could be construed as representing an "energy-time uncertainty relation?" Does there exist any reference to such a prediction, or ...
1
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4answers
129 views

What does “spread of momentum” actually mean?

I was reading Feynman's lecture in which Feynman invoked his own way of explaining the uncertainty principle using single-slit experiment. There I found: To get a rough idea of the spread of ...
2
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1answer
67 views

Why does $tr \ e^{-\frac{i}{h}\hat{H}t}= \int d^nr \left< \textbf{r}| e^{-\frac{i}{h}\hat{H}t} | \textbf{r} \right>$ hold?

I would like to consider the trace of the time evolution operator $e^{-\frac{i}{\hbar}\hat{H}t}$ Apparently in single-particle quantum mechanics is can be represented as $$ tr \ ...
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0answers
25 views

Does the shell structure really make sense for a high-Z atom?

The shell structure picture is based on the mean field approximation, which replaces the interaction between the electrons by some mean-field potential. For a high-Z atom, like Fe, or even Ur, is the ...
5
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2answers
361 views

Does the $\frac12mv^2$ law apply to quantum mechanics?

Consider the classical Hamiltonian for a spring: \begin{equation} H = \frac{1}{2}\frac{p^2}{m} + \frac{1}{2}kx^2 \end{equation} This is one of those simple cases where when you work out the math we ...
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2answers
135 views

How can I prove following density matrices have same eigenvalues?

I have the following two density operators, the paper I am reading says that these two operators have same eigenvalues $$\rho^i = \frac{1}{3} ( |0\rangle \langle 0 | +|1\rangle \langle 1 |+|2\rangle ...
2
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1answer
35 views

Product on Tensor Products

I'm trying to understand how products on tensor products work. For instance, in quantum mechanics, you have ($x$ tensor $y$) times ($z$ tensor $a$), where $x$, $y$, $z$, $a$ are all operators acting ...
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2answers
48 views

Is lightning an example of energy emision from accelerated charge?

I have always heard that the inconsistency in explaining atomic models with classical mechanics was that the study of electrical charges had shown that whenever a charge is accelerated, it emits light ...
0
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2answers
82 views

multiverse fabric of reality

Source-"fabric of reality"- author d. deutsch - his contention, as I understand it, is that quantum interference is caused by "almost, but not identical quite quantum entities" , e.g. electrons, from ...
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1answer
71 views

What are the consequences of ignoring non-physical solutions?

a particle in a finite width 1 - D quantum well, produces 2 math solutions outside the well walls ( $e^{bx}$ and $e^{-bx}$,( ignoring normalising factors.) The decaying function, $e^{-bx}$, is used ...
0
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1answer
86 views

How much information does the Hamiltonian contain in quantum mechanics? [closed]

Given a Hamiltonian, let's say of a many-body system, through the Schrodinger equation,in principle we can find the eigenfunctions and their corresponding eigenvalues (spectrum). Now given an ...
2
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2answers
96 views

Why we cannot describe operator for force $F$ in quantum mechanics?

In quantum mechanics we describe operators corresponding to momentum but we don't define operator for force what is the reason behind it?
3
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2answers
146 views

Why are neutron absorption cross sections high at low incident energy?

For example, U-235 fission cross section looks like this: As I understand it, the resonances peaks correspond to discrete quantum states of the excited compound nucleus. As you go higher, the ...
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0answers
34 views

Problems and applications of Topoligcal Insulators today [closed]

I am learning about topological insulators in my applications of quantum mechanics class and i was wondering why exactly are they important? Who cares if the material only conducts on the surface? ...
1
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0answers
94 views

What does it mean when it is said that “General Relativity and Quantum Mechanics are incompatible”? [duplicate]

In many of the pop-science-y documentaries on theoretical physics I often hear the statement: "General Relativity and Quantum Mechanics are incompatible" Some googling tells me that "General ...
0
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2answers
169 views

Light, being a probability wave, carries energy; does an electron wave also carry energy? If so, how?

The entity "light" behaves as a wave & particle. The wave is actually probability wave . That is, to every point in a light wave we can attach a numerical probability that a photon can be ...
0
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2answers
50 views

Why is the imaginary unit conventionally put on the right hand side of commutation relations? [closed]

Commutation relations in quantum mechanics are usually written in the form $$ [x_i,p_j] = i \hbar \delta_{ij} $$ with the imaginary unit $i$ put on the right hand side of the equation. But ...
2
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6answers
157 views

Rutherford's gold foil experiment: can alphas be deflected by electrons vs. nucleus?

In this experiment, is it possible that some of the alpha particles are deflected by the electrons? Gold, after all, usually also has ~79 of them in each atom. Since the alpha particles want ...
1
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2answers
147 views

Having Trouble Understanding Feynman Diagrams [closed]

So recently I have became interested in quantum physics. However when I read up on quantum physics Feynman diagrams appear everywhere, and I do not understand them! Here is a Feynman diagram that is ...
0
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0answers
29 views

Any importance of $i$ before the time reversal operator for spin-1/2 system?

I've read about that: For systems with spin 1/2, time-reversal symmetry has the operator $\mathcal{T}=i\sigma_y K$. I wonder if the imaginary unit $i$ has any importance. Without $i$, ...
2
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1answer
52 views

Pion decay into electron and anti-neutrino

In Peskin and Schroeder Books Chapter 5 subsubection Bound State equation (5.43) $\mathcal{M}(\uparrow \uparrow \rightarrow B)=\sqrt{2M}\int ...
1
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1answer
36 views

Centrifugal Term

I'm studying quantum mechanics with Griffiths (2 nd edition) and I have one question related to the Schrodinger equation in spherical coordinates. In the radial equation: ...
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0answers
38 views

Quantum Localization

Hi every body, Could someone please give me clarification and explanation about localization, localization length and Quantum localization? All i know is that it has something to do with diffusion. ...
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0answers
46 views

Corrections to the Equipartitio theorem

Does anyone know why sometimes $E = \frac{3}{2}k_{b}T $ is written as $E = \pi k_{b}T$. Where does this come from?
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1answer
36 views

Why does a quantum cloner imply superluminal communication

I am wondering why superluminal communication would be possible if a quantum cloner would exist? The common argument (FLASH) goes as follows: Alice and Bob share the Bell state $$ |\psi^-\rangle = ...
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1answer
23 views

How to prepare the Stern-Gerlach experiment for a particular state

If we want to form a diagram or calculate the angles at which the magnets need to be positioned in the Stern-Gerlach setup,how do we proceed? For example, if I want to prepare the following state, ...
0
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2answers
56 views

Probability from classical physics compared with quantum mechanics [closed]

$|\psi\rangle$=$\frac{1}{\sqrt5}|\uparrow_z\rangle+\frac{2}{\sqrt5}|\downarrow_z\rangle$ a)What is the probability of obtaining $+\frac{\hbar}{2}$ for $S_x$? b)If after obtaining ...
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0answers
23 views

Probability from classical physics compared with quantum mechanics [duplicate]

$$|\psi\rangle=\frac{1}{\sqrt5}|\uparrow_z\rangle+\frac{2}{\sqrt5}|\downarrow_z\rangle$$ a)What is the probability of obtaining $+\frac{\hbar}{2}$ for $S_x$? b)If after obtaining ...
2
votes
2answers
107 views

An attempt to understand Quantum mechanics [closed]

Can I learn quantum mechanics just by knowing basic calculus and algebra? I know basic differential calculus and integral calculus. I am willing to study to understand what quantum mechanics means. ...
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0answers
17 views

With quantum entanglement, why does the spin of a particle depend upon probability when measured is at an angle?

In this video https://www.youtube.com/watch?v=ZuvK-od647c it talks about how the particle's being spin up or down when measured at an angle depends on this probability: cos^2(theta/2). Why is it ...
45
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1answer
4k views

Is it possible to “see” atoms?

As per my knowledge, atoms are small beyond our imaginations. But there is an image on Wikipedia that shows silicon atoms observed at the surface of silicon carbide crystals. The image: How can we ...
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0answers
36 views

Hamiltonian for semiconductor

I was wondering which terms we need in a semiconductor Hamiltonian where no transition between the valence and conduction band occur? First we would have a term describing the energy of the full ...
1
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0answers
52 views

How to find creation and annihilation operators? [duplicate]

I get 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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1answer
53 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 ...
5
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4answers
328 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 ...
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votes
1answer
59 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 ...
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0answers
20 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 ...
0
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1answer
25 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 ...
3
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0answers
113 views

Why is imaginary time “outdated”? [closed]

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 idea deliberately avoided in modern ...
1
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1answer
31 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 ...
0
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0answers
31 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 ...
0
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1answer
64 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
38 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
40 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 ...
0
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3answers
60 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 ...
0
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2answers
36 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
48 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
22 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 ...