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
226 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 ...
6
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3answers
375 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
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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
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3answers
237 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
433 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 ...
13
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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 ...
12
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2answers
1k 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 ...
4
votes
2answers
247 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?
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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
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2answers
572 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
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0answers
268 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
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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 ...
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1answer
9k 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
516 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
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1answer
211 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? ...
5
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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 ...
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3answers
817 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 ...
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1answer
423 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
728 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
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1answer
646 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 ...
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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
546 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 ...
9
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2answers
283 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 ...
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0answers
40 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
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1answer
134 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
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2answers
1k 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
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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
248 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
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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 ...
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0answers
279 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 ...
16
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2answers
1k views

Why doesn't the no-cloning theorem make lasers impossible?

As I understand lasers, you start off with a few photons that are in an identical state, and other photons that are created later tend to have the same quantum numbers due to Einstein-Bose statistics. ...
3
votes
1answer
125 views

Quantum Cascade Laser [closed]

I want to learn about quantum cascade laser in a six month time. Can anyone please suggest me any reading materials or video lectures. I have background in calculus and linear algebra. I am learning ...
2
votes
0answers
116 views

Second quantization with qubits

Is "second quantization" means system wich can contain variable, unknown, superposed and otherwise uncertain number of qubits? Can "second quantized" system contain 0.5% of 1 qubit and 95% of 2 ...
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0answers
79 views

Nonlocal games: The CSCH game

The problem that I am having is that I don't see how they come up with the probabilities mentioned on Slide #7 here: https://www.ipam.ucla.edu/publications/opws1/opws1_9367.pdf first I don't ...
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votes
1answer
108 views

Some complex-number manipulation when calculating coefficients

I am going through Sakurai's quantum mechanics, and at one point the solution to a problem says: $(\sin(\beta)\cos(\alpha)-i\sin(\beta)\sin(\alpha))b+\cos(\beta)a=a$ ...
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0answers
938 views

Scattering Amplitude in second Born Approximation for the Yukawa potential

Does anyone know where I can find the analytical expressions of the scattering amplitude in second Born Approximation for the Yukawa potential? I need it for the both cases of the method of partial ...
1
vote
3answers
147 views

What are correlated magnetic moments?

My book has the following sentence and I don't understand what correlation or lack of correlation means: At high temperature the magnetic moments of adjacent atoms are uncorrelated (to maximize ...
3
votes
0answers
73 views

Infinite quon statistics/Quantum Boltzmann statistics: models and hamiltonians

I learned long ago that there are some exotic classes of statistics. One of them is calleq $q$-on or quon statistics. It is given by $$a_ia^+_j-qa^+_ja_i=\delta_{ij}$$ Infinite statistics (Quantum ...
2
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2answers
997 views

Magnetic moment of electron

Since magnetic moment come from the circulation of charge, what is the origination of the electron's magnetic moment? Because spin of electron is not the classical spin of particle. Can we say that ...
1
vote
2answers
176 views

Transition integral from 1-D cartesian into 3-D polar coordinate system

Lets say we have an electron which can be in two states. Its wavefunction for two states is then $\Psi=A\Psi_n + B\Psi_m$, where $\Psi$ is time dependent wave function. I know that the transition ...
0
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0answers
389 views

Can the laws of classical mechanics be derived from quantum mechanics? [duplicate]

Can classical mechanics be derived from quantum mechanics as the same way thermodynamics derived from statistical mechanics?
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1answer
242 views

Is there any quantum analogs of three body problem?

IS there any quantum analogy where a three state (or three body) system shows chaotic dynamics as three body problem in classical mechanics?
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2answers
192 views

Non-locality and Bell's theory

Non-Locality – (just ) one more question? I have read comments that Bell’s theory proves quantum mechanics is non-local, and also comments that it does not. I have read a comment by a very eminent ...
2
votes
1answer
754 views

What is the preferred basis objection to the many-worlds interpretation of quantum mechanics?

I've seen the preferred basis problem referred to in many places, but have not seen a clear explanation of what the problem is. For example, this question asks whether the problem has been solved, but ...
2
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2answers
339 views

Many-worlds interpretation vs 'just' randomness?

I have this question about MWI I always wanted to ask but never dared to! It could be that I just don't know enough physics to understand the answer, or the question! Anyway, here goes: What is it ...