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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Group Velocity of guassian packet equals time derivative of mean position?

If I look at a gaussian wave package, and then interpret (in the usual Quantum-Mechanics Way) its square value as the propability density, then I can calculate a mean value for the position: $$ x_{...
1
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0answers
27 views

What is the difference between active and passive transformations in Quantum Mechanics?

I am trying to understand what each transformation means and what their differences are but many books that don't state which transformation they are referring to make it a bit confusing to understand ...
10
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1answer
311 views

In quantum mechanics, how exactly do we associate Hermitian operators to classical observables? [duplicate]

In a first course on quantum mechanics, everybody learns some version of the following statement: Postulate: To every classical observable $A$ of a physical system, there corresponds a Hermitian ...
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0answers
11 views

Selection rules for electric quadrupole radiation

The selection rules for electric quadrupole radiation in a Hydrogen-like atom are: $$ \begin{aligned} \Delta l &= 0,\pm2 \hspace{1cm}(l=0\leftrightarrow l'=0 \textrm{ is forbidden}) \\ \Delta m &...
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0answers
66 views

What does the Free Will Theorem Imply?

Sorry if discussion of the Free Will Theorem belongs in the philosophy section, but as it is in the realm of physics too, I thought I would post it here instead... If we have a free will in the ...
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2answers
52 views

How do we determine the location of particles?

Can someone explain how the location of a particle is determined both theoretically and experimentally (if possible)? Can the location of a particle be given by the uncertainty principle? (dividing ...
3
votes
1answer
42 views

Can Light Waves Be Irregular?

From what I understand, electromagnetic radiation produced by an antenna is of the frequency that corresponds to the motion of the electrons moving around in the antenna. And I assume that the ...
0
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1answer
61 views

Applying angular momentum operator [on hold]

How are the algebraic steps to applied the angular momentum operator defined as: $$\hat{L}=-i\hbar[r\times\nabla]$$ to $$\Psi=a~ \psi_{431}$$ where the $\psi_{nlm}$ are the eigenfunctions of the time ...
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0answers
5 views

Calculating 2 particle Partial Trace for Density Matrix in Zeeman basis for a large number of Spins

I want to trace out all spins but 2 from a density matrix in the zeeman basis for N spins. For N=3 for example I would have the basisvectors: $ |S=1.5, m=-1.5\rangle =|000\rangle, |S=1.5, m=1.5\rangle ...
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0answers
29 views

Average magnetic dipole moment [on hold]

An electron in the hydrogen atom is described by the wavefunction: $$ \Psi = 0.5773\left(\psi_{431} + \psi_{432} + \psi_{321} \right) $$ where the $\psi_{nlm}$ are the eigenfunctions of the ...
0
votes
1answer
50 views

How to make an intuitive sense of the definition of Hermitian adjoint? [on hold]

How to make an intuitive sense of the definition of Hermitian adjoint? Why it is defined in that way? What is the different between operators and matrices?
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28 views

Relative velocity between phase velocity wave and a group velocity wave

It is said that material particles have a dual nature. A particle is associated with a wave which travels with phase velocity and the particle travels with group velocity. These are related by $$v_\...
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26 views
0
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1answer
26 views

Number of electrons in conduction band

As mentioned in a previous question, the number of electrons in conduction band in a semiconductor can be computed as follows: $$N = \int_{E_c}^{+\infty} g_c(E)f(E)dE$$ where $g_c(E)$ is the density ...
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0answers
29 views

Is my understanding of creation/annihilation operators' functional dependency correct?

I am trying to gain a little intuition about second quantisation, specifically about creation/annihilation operators. Lets say you quantise the free EM field (in 1d) and end up with the usual: $H=\...
2
votes
1answer
95 views

How to evaluate possible values of spin of two photon system?

Photon hasn't well defined quantity such as spin. Instead of it, it is characterized by helicity $h$. Let's assume state of two photons in CM frame (with $\mathbf k$ being the momentum of one of ...
-2
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0answers
30 views

what is the rough motion of an electron in an atom [duplicate]

If The Uncertainity principle is true,then how does an electron move ?if the motion cannot be random also,then how does it occur?
11
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4answers
571 views

Curvature of Hilbert space

That may appear as a dumb question, but: Does Hilbert space have curvature, or is it a flat space? How and why?
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1answer
40 views

Uncertainty and Classical waves

My professor, introducing Heisenberg uncertainty principle, started from the Fourier transform and the classical uncertainty for waves. He told about the localized impulsive wave $\delta(x)$ which ...
3
votes
1answer
25 views

What happens to the energy of fermions when a degenerate gas forms?

For example, when an electron degenerate gas forms, two electrons (of opposite spins) occupy each of the lowest possible energy states up to the Fermi energy. This is because of the Pauli exclusion ...
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2answers
32 views

Understanding Zeeman Splitting

I'm reading a standard modern physics history book ("Inward Bound" by A. Pais), and I realized I don't really understand Zeeman splitting well. In the section I'm reading, there's a short discussion ...
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0answers
39 views

This might make no sense light is time [on hold]

I've done a lot of research on time I think when light/color is absorbed it is giving off as time and when it is going fast the light can't keep up
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0answers
50 views

Expectation value of an Observable and Eigenstates

I am learning about Quantum Mechanics at the moment and I was wondering about Eigenfunctions and Observables. The question I would like to ask is, If a wavefunction is not an eigenstate of an ...
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3answers
105 views

Significance of wave number?

Till now all I know about the wave number is its formula i.e. ${\frac{2\pi}{\lambda}}$. I always wanted to know what it really means. So can anyone please, explain me its physical significance?
6
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1answer
70 views

One particle states in an interacting theory

Question: What is the general definition of one particle states $|\vec p\rangle$ in an interacting QFT? By general I mean non-perturbative and non-asymptotic. Context. 1) For example, in Weigand'...
2
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0answers
49 views

$\left< \frac{\partial (xp)}{\partial t} \right> = 0$ When is this true?

Is this always true in quantum mechanics? $$\left< \frac{\partial (xp)}{\partial t} \right> = 0$$ I encountered this when working problem 3.31 in Griffiths Introduction to Quantum Mechanics II....
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0answers
16 views

Why must the separation constant be real in a time dependent wave function?

I'm not sure if I'm asking this right. I'm reading ''Introduction to Quantum Mechanics'' by Griffiths and in the chapter 2 exercises he asks to prove that the separation constant, $E$, must be real. ...
6
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8answers
2k views

Prove that an electron in a hydrogen atom doesn't emit radiation [duplicate]

According to electrodynamics, accelerating charged particles emit electromagnetic radiation. I'm asking myself if the electron in an hydrogen atom emits such radiation. In How can one describe ...
3
votes
2answers
92 views

The meaning of 'coupling'?

In quantum mechanics if two quantities $A$ and $B$ are said to be coupled what does this actually mean? I would guess that it means we have a term like $A\cdot B$ in the Hamiltonian but this is only ...
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0answers
32 views

quantum mechanics problem orthonormal function [on hold]

$$\psi_n(x)=\sqrt{\frac{2}{a}}\sin\left(\frac{\pi n}{a}x\right)$$ is this wave function orthonormal or not? If yes then prove it.
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1answer
66 views

Practical way of expressing the $\delta$-function [on hold]

I have got a problem in using the $\delta$-function. As we know, this function is often used to define a 'density'-related quantity. Such as the density of states or some correlation function. Take ...
1
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1answer
68 views

Is the MWI symmetric in time?

Reading the blog of Sean Carroll (I recognize he isn't the only voice) has made me more sympathetic to the notion of many worlds, but reading Susskind (also not the only voice) has made me think that ...
4
votes
2answers
760 views

What causes Potassium to decay into Argon the way it does

From evolutionwiki: "Potassium 40 decays into argon 40 through a process known as electron capture. In electron capture, an electron from the innermost electron shell "falls" into the nucleus, ...
-4
votes
2answers
48 views

How to resolve “bottleneck” of encoding input of quantum computer? [on hold]

As far as I understand, all quantum computing purpose is to accelerate exponentially (upon input length) computation time of given task. But here user faces bottleneck to serialize input, and ...
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0answers
40 views

Are Fock spaces just a special type of tensor algebra?

Are Fock spaces just a special type of tensor algebra? The definitions I am using: http://en.wikipedia.org/wiki/Fock_space http://en.wikipedia.org/wiki/Tensor_algebra From what I can tell, the ...
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0answers
33 views

Eigenkets in matrix representation [on hold]

We use base kets in matrix representation of an operator $X$. Could the base kets be possibly be eigenkets also, of operator X? (Here, I'm taking X as a general operator , not only observable,i.e. ...
0
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0answers
27 views

Balancing a Quantum mechanical pencil [duplicate]

I have tried to solve the question given in Sakurai quantum mechanics book about what is the maximum time you can balance a pencil on its tip using the uncertainty principle. Classical pencil is in ...
-5
votes
1answer
44 views

Communication via teleportation/entanglement (FTL communication)

I know this has been asked many times, but I have a hard time "crystallising" it in my mind. First: let's say we teleport a DVD (with quantum teleportation). Isn't this FTL communication? Second: ...
5
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2answers
83 views

Uncertainty Relations, Conjugate Quantities, and Fourier Transforms

I've heard from a lot of people that the reason momentum and position have an uncertainty relation is because of the Fourier Transform. But is this in any way the case? If it were I would expect all ...
0
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1answer
25 views

Potential step and tunnelling

Imagine a particle with energy $E$ heading towards a potential step with height $V_0$ where $E<V_0$. The particle's wave function is oscillatory before the boundary and exponentially decaying in ...
0
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0answers
30 views

Can we see interference if move screen? [closed]

In interference using electrons in double slit experiment, we cannot use light source, as it disturbs apparatus. But, can't we simply move screen towards and away from screen, to know where they ...
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0answers
18 views

Uncertainty principle-QM [duplicate]

I some trouble understanding the uncertainty principle. I understand most of the math derivation but not the physics. Is there any intuitive explanation of this idea, and why is the uncertanty does ...
0
votes
2answers
47 views

What is a magnetic line of force? [on hold]

Do magnetic limes of force 'flow'? If so, what is it that is flowing? What is the 'line of force' composed of?
1
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0answers
65 views

Generalisation of a particle in QFT

In classical mechanics, we assumed a particle to have a definite momentum and a definite position. Afterwards, with Quantum mechanics, we gave up the concept of a time-dependend position and momentum, ...
3
votes
2answers
52 views

Moving of spin up and spin down electrons in a magnetic field [on hold]

Suppose we have an electron in a conducting space, and now we apply a magnetic field. Now according to the right hand rule, the electron will have a circular motion in the plane perpendicular to the ...
2
votes
3answers
57 views

Two qubits system in polar co-ordinates

I know that I can write a single qubit state in terms of polar co-ordinates $(r,\theta,\phi)$ on a Bloch sphere. \begin{equation} \rho = \begin{pmatrix} \frac{1+r \cos\theta}{2} &\frac{r \exp(-i\...
0
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0answers
13 views

Spin half particle Magnetic field oriented along y-axis

I've been looking over past papers for an upcoming QM exam and have had a few issues wrapping my head around this question. I can follow the common example as seen in Griffiths where the field is ...
6
votes
2answers
158 views

Why hermitian, after all? [duplicate]

This question is going to look a lot like a duplicate, but I've read dozens of related posts and they don't touch the subject. Here we go. Why are observables represented by hermitian operators? ...
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0answers
32 views

Luminiferous æther = quantum's “vacuum”? [closed]

How is the luminiferous ether, which relativity theory disregarded, different from and similar to what in quantum mechanics is called "the vacuum"?
2
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2answers
53 views

Does QFT modifies Quantum Mechanics? [duplicate]

The basis of Quantum Mechanics is contained in the postulates which tell us how to describe quantum systems (below I disconsider possibly degenerate spectra just for simplicity): To describe a ...