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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2answers
378 views

Are Rabi oscillations a pure quantum process?

Rabi oscillations are commonly known as the oscillations in time of the occupation probability of a quantum two-level system under the action of a coupling interaction between the two-levels. ...
4
votes
3answers
675 views

Are negativity of the Wigner function and quantum behaviour equivalent?

I've read the following question: Negative probabilities in quantum physics and I'm not sure I understand all the details about my actual question. I think mine is more direct. It is known that the ...
2
votes
1answer
127 views

Sinusoidaly Driven Two-Level System (TLS)

I'm trying to solve the driven Two-Level System (TLS or qubit) question using a Fourier transform of the Schrodinger equation (SHE), but I'm getting stuck on solving the equation. Given Hamiltonian ...
2
votes
1answer
806 views

Hydrogen ground state energy calculation?

We want to find the energy of a hydrogen atom ($Z=1$) in the ground state $$ \psi_{100} = \frac{1}{\sqrt{\pi}}e^{-r}\ \ \ \ \ \ (\mbox{atomic units}) $$ with Hamiltonian $$ H = -\frac{1}{2}\nabla^2-\...
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2answers
227 views

The irreducible observer

This question probably verges on pseudo-science and probably sounds like gibberish, so please pardon me. But I'll ask it anyway. In an ideal lab experiment there is generally a separation between the ...
1
vote
1answer
710 views

Calculating expectation value

I am trying to calculate the expectation value of an infinite quantum well in one dimension (L). Given: $$\phi_n = \sqrt{\frac{2}{L}}\sin\left(\frac{n\pi}{L}x\right)$$ and $$E_n=\left[\frac{\hbar^2\...
1
vote
1answer
357 views

How does the uncertainty principle make a photon beam spread out?

I'm reading about uncertainty principle, and something has been bothering me for quite a while. There is the formula: $$\sigma_x \sigma_p \ge \frac{\hbar}{2}$$ I know what this means: the more you ...
8
votes
3answers
1k views

How does QFT help with entanglement?

I'm a bit confused. QFT is claimed to incorporate both Quantum Mechanics and Special Relativity. Therefore it should address the problem of non-locality caused by entanglement. However when I search ...
3
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0answers
212 views

Measure energy state of quantum harmonic oscillator

When discussing the quantum mechanical harmonic oscillator we are talking about energy eigenstates. How would one actually measure in which state an harmonic oscillator is in? Could you weigh it and ...
2
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1answer
104 views

Does Heisenberg uncertainty apply within each quantum configuration, or in the amplitude distribution over them?

I'm still absorbing some basic ideas about quantum physics and now I think I have to reconsider the Uncertainty Principle. Here is what I understand, in summary: a "configuration" specifies the ...
1
vote
2answers
358 views

A simple question on $SU(2)$ gauge transformations in Wen's papers on projective symmetry group (PSG)?

Recently I am studying the projective symmetry group (PSG) and the associated concept of quantum order first proposed by prof.Wen. In Wen's paper, see the last line of Eq.(8), the local SU(2) gauge ...
0
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1answer
146 views

Some questions regarding the behaviour of electrons [closed]

If I understand correctly: An atom acts a potential well for the electrons -- and particles in a potential well have discrete energy levels. There is a non-zero minimum to this energy called the ...
9
votes
1answer
1k views

The vacuum in quantum field theories: what is it?

In Section 10.1 of his textbook Quantum Field Theory for Mathematicians, Ticciati writes Assuming that the background field or classical source $j(x)$ is zero at space-time infinity, the presence ...
0
votes
0answers
156 views

A simple question on the projected wave function?

For example, consider a spin-1/2 AFM Heisenberg Hamiltonian $H=\sum_{<ij>}\mathbf{S}_i\cdot\mathbf{S}_j$, and we perform a Schwinger-fermion($\mathbf{S}_i=\frac{1}{2}f^\dagger_i\mathbf{\sigma}...
1
vote
0answers
157 views

What do 'first moment' and 'second moment' of a canonical operator mean?

Can anyone explain to me what the first and second moments of a canonical operator mean, in the context of 1D harmonic chain? Thank you!
3
votes
2answers
229 views

Space translation of operators, states, and particle densities

In Sidney Coleman's Lectures he talked about space translations such that $$\tag{1} e^{ia P}\rho(x) e^{-ia P} ~=~ \rho(x-a),$$ but when I expanded the exponentials and used the commutation relation ...
7
votes
3answers
422 views

Is entanglement necessary for quantum computation?

Is entanglement necessary for quantum computation? If there was no error in the computation,superposition of states would be sufficient for quantum computation to be carried out.Is this right?
2
votes
3answers
5k views

Necessary condition for square integrable functions?

I'm studying Quantum Mechanics and I came across this which I don't quite understand: For a vector space of functions $f(x)$ to be square integrable (i.e $\int{|f(x)|^2dx < \infty)}$, the necessary ...
2
votes
3answers
247 views

Uncertainty principle and multiple observers

My understanding is that an observer can measure the precise location of a particle so long as the corresponding uncertainty in momentum measurement is not an issue and vice-versa. Say there is ...
1
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1answer
442 views

Perturbation theory

I am puzzled with perturbation theory when studying quantum mechanics and solid theory. What I learn about perturbation is, from my ignorant point of view, just mathematics, or even simpler, matrix ...
14
votes
2answers
2k views

Does every hermitian operator represent a measurable quantity?

In Quantum mechanics, observables are represented by hermitian operator. But does every hermitian operator represent a observable? If not , how do we know that whether a hermitian operator represent ...
13
votes
2answers
2k views

How is the Schroedinger equation a wave equation?

Wave equations take the form: $$\frac{ \partial^2 f} {\partial t^2} = c^2 \nabla ^2f$$ But the Schroedinger equation takes the form: $$i \hbar \frac{ \partial f} {\partial t} = - \frac{\hbar ^2}{...
4
votes
2answers
253 views

How does electron know when to change into a wave?

It is known that electron behaves as a wave also. How does electron know that it has to change into a wave? Are there any factors that influence the behavior of electron changing into wave?
1
vote
1answer
59 views

A projector equal to its own conjugate by a unitary

For projector $p$, in finite dimension say, some unitaries $u, v$ does $upu^\dagger = vpv^\dagger$ implies $u = v$ ? Intuitively, can we not say that a unitary is matrix permuting the basis and since $...
5
votes
2answers
612 views

In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?

Isham & Doering have written a series of papers exploring how to ground physics in topoi. Now the internal logic of topoi is higher order typed intuitionistic logic. In their theory what role is ...
1
vote
0answers
283 views

Distinguishing between an entangled and non-entangled state (mainly $S(H_A) \otimes S(H_B)$ vs. $S(H_A \otimes H_B)$)

Say I have two quantum systems $A$ and $B$ I can look at the joint (composite) system $AB$ which is given by $H_{AB} \in H_A \otimes H_B$ Measuring a subsystem with respect to a collection of ...
2
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0answers
57 views

Pseudo-randomness of observables

There is a somewhat recent paper by Colbeck and Renner that, given the assumptions — 1) QM accurately predicts the correct statistical results in experiment (which so far has always been found to be ...
3
votes
1answer
2k views

Decay of metastable state: spontaneous vs. stimulated emission.

I have a question about the upper laser level (the metastable level) in a 3-level laser system. I will call the ground level of the 3-level laser system by "g" and the metastable level by "m". The ...
0
votes
1answer
104 views

Space and Time Equality and information transfer between particles existing at different time

Since space and time are the same is it that whatever happens at different positions in space should take place at different time? If what I think is correct consider an electric dipole, the charges ...
-2
votes
1answer
10k views

What causes electron to orbit the nucleus in an atom? [closed]

What causes the electron to orbit the nucleus? Which is the force that causes it to do so? Is it related to the Electro - Magnetic force? .
3
votes
2answers
531 views

Physical intepretation of nodes in quantum mechanics

I am taking my second course in QM, and my head is starting to spin as it probably should. But I would very much like to clear up my head about a few details regarding the wave function. As I know it ...
2
votes
1answer
215 views

superposition of two states with different number of particles

In an electron gas with no mechanism of production or destruction of electrons is it possible to prepare an state which is superposition of states with different number of electrons? $|\psi\rangle=|N=...
5
votes
1answer
2k views

Understanding the partial trace and deriving $\langle l|R_{B}|k\rangle = \text{Tr}((\mathbb{I}_{A} \otimes |k\rangle \langle l|)(R_{AB}))$

By definition according to the notes I am looking through: The partial trace $\text{Tr}_A:L(H_A \otimes H_B) \rightarrow L(H_B)$ is the unique map that satisfies: $$\text{Tr}(L_B \cdot \text{Tr}_A(R_{...
0
votes
3answers
839 views

Why can the Schroedinger equation be used with a time-dependent Hamiltonian?

I have a puzzle about Schroedinger equation with time-dependent hamiltonian, which is usually used in time-dependent quantum systems. However, one of the axioms in quantum mechanics postulates that ...
1
vote
1answer
434 views

What is a ket of a vector with a bra of another one?

Suppose we have an orthonormal basis $\{ \psi \}$ in finite dimension of a hilbert space; What is the butterfly operator of a sum of the $ \psi $, say $\psi_i +\psi_j$ ? Since by linearity of "...
5
votes
1answer
771 views

Intuitive understanding of the irreps like Wigner-D matrix?

Wikipedia defines Wigner D-matrix as an irreducible representation of groups SU(2) and SO(3). What is a good way to visualize this representation? Is there any physical system which can be kept in ...
5
votes
1answer
678 views

Do mutual eigenkets imply commutation of two operators?

I have been working on this question. I have solved it, and I would like to check whether my line of reasoning is right or wrong Question: Prove that if there exists a mutual complete set of ...
1
vote
0answers
56 views

Casimir Effect and polarization of photons

I have read Casimir's derivation of the Casimir fore between 2 parallel plates and have been told that in reality, the Casimir force should be twice as large due to the 2 polarization states of ...
2
votes
2answers
553 views

accelerated charged particles and interaction with magnetic field

In high school we are taught that magnetic field perpendicular to velocity of an charged particle experience perpendicular force that causes it to move in circular path by relation $$qvB=\frac{mv^2}{r}...
9
votes
2answers
295 views

Can I treat a quantum process as a Markov process?

When I learned classical Markov process, I noticed some similarity of quantum process and Markov process, and the only difference of them is between probability and probability amplitude whose modulus ...
1
vote
0answers
41 views

QM -group reps and transforming wavefunctions

QM texts seem to have many ways of motivating the angular momentum operators and deriving the l and m quantum numbers . But the connection between physical rotaions in 3 dim space and an operator in ...
7
votes
1answer
138 views

No-cloning theorem with 3 particles

I know how to demonstrate that it is not possible to make a unitary operator so that $|a\rangle|0\rangle$ turns into $|a\rangle|a\rangle$ , but is it possible to have $|a\rangle|0\rangle|0\rangle \...
12
votes
2answers
2k views

Why does the classical Noether charge become the quantum symmetry generator?

It is often said that the classical charge $Q$ becomes the quantum generator $X$ after quantization. Indeed this is certainly the case for simple examples of energy and momentum. But why should this ...
3
votes
0answers
151 views

What does “quantum theory forbids promiscuous entanglements” mean?

The context is this article about black hole firewalls. The phrase appears on page 3. It appears to be saying that only pairs of particles can be entangled, never multiple particles, and that this ...
8
votes
1answer
2k views

What is mean by 'good quantum number' in spectroscopy?

In electronic spectroscopy of molecules, why some quantum numbers are considered to be 'good quantum numbers'? For example, $n$ and $l$ are said to be not good quantum numbers while $j$ is considered ...
2
votes
0answers
269 views

Uncertainty Principle and Bohmian mechanics

The Uncertainty Principle is a relationship between measurements of pairs of attributes, position and momentum, as well as energy and time. Perfect precision of one attribute's measurement leads to a ...
2
votes
0answers
124 views

How to understand the transmission coefficient from the following question?

I want to understand the transmission coefficient and construct a time-independent Schrodinger equation where $$ V(x)=\left\{ \begin{array}{c c} \delta(x), & |x| < 1 \\ + \infty, & ...
1
vote
1answer
107 views

What is it called when two particles are associated so that what happens to one happens to the other?

There was some experiment that I read about some time back in which two particles (or the same particle, but split into two) were sent in opposite directions, but when something happened to one, it ...
4
votes
4answers
1k views

Why are the classical electron radius, the Bohr radius and the Compton wavelength of an electron related to each other?

Using the definition of the fine-structure constant $\alpha = \frac{4 \pi \epsilon_0 \hbar c}{e^2}$ and the Compton wavelength of an electron $\lambda_c = \frac{h}{m_e c}$ the classical electron ...
0
votes
0answers
286 views

weak interaction coupling constant

in wikipedia, the weak interaction coupling constant is said to be 10^-13 times weaker than that of the strong interaction but hyperphysics (http://hyperphysics.phy-astr.gsu.edu/hbase/forces/couple....