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 ...
7
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5answers
179 views
Quantum mechanics and everyday nature
Is there a phenomenon visible to the naked eye that requires quantum mechanics to be satisfactorily explained? I am looking for a sort of quantic Newtonian apple.
2
votes
0answers
21 views
How to numerically solve a laser driving semi-classical two-level system using Floquet formalism?
Consider the semi-classical laser driving two-level atom, where the laser is treated classically and the atom is treated quantum mechanically. The effect of laser on the atom is a dipole coupling:
$$
...
2
votes
1answer
47 views
Interpretation of de Broglie wave
Until what point can the de Broglie wave be thought as a real wave?
I mean, is it made of something?
What amplitude does it have? Is it a sine wave?
How can it be related to the wavefunction of the ...
6
votes
0answers
62 views
What is the reason that relativistic corrections for hydrogen atom work?
Here I cite part from Sidney Coleman's lectures on Quantum Field Theory:
It is a phenomenal fluke that relativistic kinematic corrections for the Hydrogen atom work. If the Dirac equation is used, ...
3
votes
0answers
35 views
Calculating the the kernel using path integrals for quadratic lagrangians
I am reading Feynman and Hibbs on Path Integrals. In section 3.5, they show that the kernel for a lagrangian of the form $L=a(t)\dot{x}^2+b(t)\dot{x}x+c(t)x^2+d(t)\dot{x}+e(t)x+f(t)$ is ...
0
votes
0answers
28 views
fast quantum random number generator + limited decoherence rate => Schrödinger cat state?
Suppose that fast quantum random number generator (QRNG, https://qrng.physik.hu-berlin.de/) is placed in a subsystem which has limited interaction with
the rest of the world. What would happen if ...
-2
votes
0answers
27 views
Finding Clebsh-Gordan coefficient [closed]
Two electrons , their angular quantum number =1 . Find the inner product of < 2 0 | 00 > ?
0
votes
1answer
25 views
Eigenvector Grover Operator
I have a question about the eigenvectors for the evolution operator of Grover's algorithm. Let $U=R_DR_f$, where
$$\begin{align*}
R_D &= 2|D\rangle\langle D| -I_N , \\ R_f &= ...
0
votes
1answer
37 views
Eigenvalue $a_n$
Q1:
In Zetilli's book page 166 (ch. "Postulates of QM", eq. 3.1) i encountered an expression $\hat{A}|\psi\rangle = a_n|\psi_n\rangle$. I know this is an eigenvalue equation, but i have seen another ...
-1
votes
0answers
29 views
What values should the solved time-independent Schrodinger equation return? [closed]
I'm doing a project on Schrodinger's equation for my differential equations class. We solved the time independent function, and now we want to provide some examples of applying the equation by solving ...
0
votes
0answers
28 views
Scalar-fermion bound state
Is it possible to have a bound state between a scalar and a fermion? For example, a squark--anti-squark bound state, provided that the decay width is sufficiently small compared to the binding energy?
...
1
vote
1answer
96 views
Why is this not a realisable operation on a quantum system?
Let $\rho = \begin{bmatrix}\ 1&0 \\ 0&0 \end{bmatrix}$, $\rho' = \begin{bmatrix}\ 0&0 \\ 0&1 \end{bmatrix}$, $\rho'' = \dfrac{1}{2}\begin{bmatrix}\ 1&1 \\ 1&1 \end{bmatrix}$ ...
-2
votes
0answers
52 views
What is the state of contempoary Quantum Physics as a discipline? [closed]
Sometimes I take the time to read textbooks and go to talks about Quantum Physics. Most of the time I do that I am appalled at how... Badly people seem to understand QM.
I do not have formal ...
0
votes
0answers
5 views
Why is it difficult to numerically solve multi-electron time-dependent Schrodinger's equation [migrated]
It seems that people usually use the Single Active Electron (SAE) approximation to deal with a multi-electron system, transforming the problem into a single electron problem. For example, in ...
2
votes
1answer
46 views
Uncertainty Principle on System of particles
I am new to Quantum Mechanics. I read the uncertainty principle - it says there are pairs of physical quantities which can't both be determined with certainty for a particle.
My question is does the ...
0
votes
1answer
42 views
Some Dirac notation unclarities
Q1:
Ok so i have come to a point where i know that $\Psi(r,t)$ which we denote only by $\Psi$ can be represented in a Hilbert space by a vector which we denote $\left|\Psi\right\rangle$. Does this ...
-2
votes
0answers
29 views
The Hartree solution of two harmonic oscillator coupled by potential $V \propto ({\bf r}_1-{\bf r}_2)^2$ [closed]
$H={\bf p}_1^2+{\bf p}_2^2+{\bf r}_1^2+{\bf r}_2^2+x({\bf r}_1-{\bf r}_2)^2$.
$x$ is the coupling factor.
0
votes
1answer
53 views
Why is the Heisenberg Uncertainty Principle not obvious give the conservation of mass- energy?
A photons energy is given by $E=h *f$ and momentum $p=E/c$ (spin?) but the photon has no (rest) mass! Therefore it is the ultimate probing tool for looking at any mass position and velocity because ...
1
vote
2answers
88 views
Can we measure “wavefunction” of quantum particles?
We know that there is uncertainty principle, so question: can we ever measure wavefunction of particles? I do not think this is possible, but I am not sure. I guess that everything is probabilistic. ...
1
vote
1answer
29 views
what is the magnetic quadrupole operator?
To find magnetic or electrical moments in quantum theory we must calculate the expectation value of an appropriate operator. the dipoles operator are similar and is easy to find but the magnetic ...
0
votes
0answers
20 views
What is the magnetic quadrupole moment of a nucleus in cylindrical coordinates?
What is the magnetic quadruple moment of a nuclei in cylindrical coordinates?
The quadrupole moment of a nucleus is zero in spherical coordinates but in the cylindrical coordinates it can't be ...
0
votes
1answer
59 views
Periodic boundary condition on a Wave Function of a Particle in a Box
Until now solving the Schrodinger Equation for a particle in a box was relatively easy because the boundaries conditions imposed zero value on the wave function at the boundaries. But now I must find ...
5
votes
2answers
108 views
Quantum Mechanical Operators in the argument of an exponential
In Quantum Optics and Quantum Mechanics, the time evolution operator
$$U(t,t_i) = \exp\left[\frac{-i}{\hbar}H(t-t_i)\right]$$
is used quite a lot.
Suppose $t_i =0$ for simplicity, and say the ...
1
vote
2answers
47 views
Vector $\vec{z}$ and its conjugate transpose $\overline{\vec{v}^\top}$ - is it the same as $\left|z\right\rangle$ and $\left\langle z \right|$
Lets say we have a complex vector $\vec{z} \!=\!(1\!+\!2i~~2\!+\!3i~~3\!+\!4i)^T$. Its scalar product $\vec{z}^T\!\! \cdot \vec{z}$ with itself will be a complex number, but if we conjugate the ...
1
vote
1answer
38 views
How do particles become entangled?
A person asked me this and I'm just a lowly physical chemist.
I used a classical analogy (how good or bad is this and how to fix?)
Basically, light has a net angular momentum of zero, insofar as ...
0
votes
0answers
17 views
Showing that the CHSH inequality is not violated
I can usually work out whether CHSH inequality is violated when the observables that we are measuring and the state we are in is given explicitly, but I'm struggling with the generality of the ...
13
votes
2answers
168 views
Is every quantum measurement reducible to measurements of position and time?
I am currently studying Path Integrals and was unable to resolve the following problem. In the famous book Quantum Mechanics and Path Integrals, written by Feynman and Hibbs, it says (at the beginning ...
0
votes
0answers
38 views
What does the difference in odds for Bell's inequality tell us about quantum mechanics?
Bell's inequality defines a lower bound for agreement/disagreement between entangled particles. When the experiment is conducted it shows lower odds.
What does this tell us? Is it possible that we ...
3
votes
1answer
120 views
Change of basis in non-linear Schrodinger equation
At the mean-field level, the dynamics of a polariton condensate can be described by a type of nonlinear Schrodinger equation (Gross-Pitaevskii-type), for a classical (complex-number) wavefunction ...
0
votes
0answers
74 views
Prove that the position operator is $\hat{x} = i\hbar \frac{d}{{dp}}$ in the momentum representation [closed]
Proof that: $x = i\hbar \frac{d}{{dp}}$
I did this, could you tell me if I am false or true
$\begin{array}{l}
x{e^{\frac{{ipx}}{\hbar }}} = - i\hbar \frac{{d{e^{\frac{{ipx}}{\hbar }}}}}{{dp}} = ...
2
votes
2answers
58 views
Is it possible to use quantum mechanics for an effective time based encryption?
This is for an application in cryptography. There is a concept called "time based cryptography", where a message can be decrypted only after a certain time, Say "12/12/2060, 12:30 GMT". There are some ...
1
vote
2answers
41 views
Time evolution of Gaussian wave packet
I'm slightly confused as to answer this question, someone please help:
Consider a free particle in one dimension, described by the initial wave function
$$\psi(x,0) = ...
11
votes
3answers
166 views
Hilbert space of harmonic oscillator: Countable vs uncountable?
Hm, this just occurred to me while answering another question:
If I write the Hamiltonian for a harmonic oscillator as
$$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$
then wouldn't one set of ...
0
votes
0answers
37 views
Question regarding operators and cylindrical coordinates
I have the following problem in my hand:
I need to arrive from the Cartesian expression $$x_{j}{\partial_{k}}x_{j}{\partial_{k}}-x_{j}{\partial_{k}}x_{k}{\partial_{j}}$$
to this expression:
...
0
votes
0answers
20 views
Does quantum mechanics depend solely on electromagnetic waves? [duplicate]
I am beginning to learn quantum mechanics. Since determining the position of an object involves probing by electromagnetic waves and since i have read a simple derivation of Heisenberg's uncertainty ...
1
vote
1answer
86 views
Matrix representation of state
This is a quantum mechanics question, I don't quite understand what it's getting at...
Suppose the we have a state described by $|1\,\,\, m\rangle$. Let its matrix representation be $\vec u$. ...
1
vote
0answers
24 views
How does a state vector change under an exchange of a boson and a fermion?
How does a state vector change under an exchange of a boson and a fermion ? That's how is $\Psi_{\alpha,\beta}$ related to $\Psi_{\beta,\alpha}$ where $\alpha$ and $\beta$ are a boson and a fermion ...
1
vote
1answer
89 views
Can 3 photons be combined to give a spin-0 projection?
Motivation: The neutral pion decays to 2 photons ($\pi^0\to\gamma\gamma$) most of the time. For the decay of the neutral to 3 photons ($\pi^0\to 3\gamma$) we have an upper limit on the branching ...
0
votes
0answers
82 views
How can it be seen that ST unifies GR and QM as the quantum gravity scale is not directly accessible
I am a newbie to superstring theories, but I came into this question:
so superstring theories purport to unify general relativity and quantum theory.
However, there is yet no definitive way to test ...
1
vote
2answers
69 views
Grover algorithm $R_D$ Circuit
I need sketch two circuits to understand Grover algorithm. The first is the operator $R_f$ and another is the operator $R_D = H^{\otimes n}(2|0\rangle\langle0|-I)H^{\otimes n}$. I get the first ...
4
votes
2answers
98 views
Why does quantum cryptography give us uncrackable codes?
Why does quantum cryptography give us uncrackable codes? What makes it 'uncrackable'? Articles in for example pop science magazines always claim QC produces uncrackable coded, however I highly doubt ...
2
votes
0answers
37 views
What is three-photon interference?
Whilst reading this paper on a quantum processor that performs a type of matrix computation, I came across the concept of 'three-photon interference'. A quick Google search shows that this process is ...
4
votes
1answer
116 views
Stark Effect on the 1st excited state of Hydrogen
I know the ground state of hydrogen is unaffected by the Stark effect to first order. And I also know that the 1st excited state is split from 4 degenerate states to 2 distinct, and 1 degenerate state ...
0
votes
1answer
58 views
How do we know superposition exists?
How do we know superposition exists? Has it been observed, or has it been deduced, and how certain are we?
The Copenhagen Interpretation seems to imply that superposition collapses into one state ...
5
votes
1answer
66 views
Do electrons need specific energies to excite electrons
Photons need specific energy levels, equal to the difference between two energy levels to excite an electron in an atom. Is this the same case with electrons that collide with atoms?
3
votes
2answers
60 views
Expanding two-variable function $f(x,y)$ over the complete sets $\{ g_{i}(x) \}$ and $\{ h_{j}(y) \}$
Quite often (see, for example, this PDF, 50 KB) when discussing the Born-Oppenheimer approximation the following assertion is made: any well-behaved function of two independent variables $f(x,y)$ can ...
0
votes
0answers
44 views
Why doublons and holons are not bounded in spin-1/2 Hubbard chain?
The Hubbard model reads
$$H = -t \sum_{\langle ij \rangle, \sigma} c_{j\sigma}^\dagger c_{i\sigma} + U\sum_i n_{i\uparrow}n_{i\downarrow} $$
In the large $U$ limit and at half-filling, the Hubbard ...
1
vote
1answer
88 views
Some Dirac notation explanations
Equation for an expectation value $\langle x \rangle$ is known to me:
\begin{align}
\langle x \rangle = \int\limits_{-\infty}^{\infty} \overline{\psi}x\psi\, d x
\end{align}
By the definition we ...
-1
votes
0answers
59 views
Quantum entanglement and speed of light $c$
On the topic of quantum entanglement, Wikipedia states:
Repeated experiments have verified that this works even when the measurements are performed more quickly than light could travel between the ...
5
votes
2answers
239 views
Your Mass is NOT from Higgs Boson
Your Mass is NOT from Higgs Boson?
http://www.youtube.com/watch?v=Ztc6QPNUqls
This guy can't be correct, right? He argues that because mostly of a nucleus' mass is made out of the space between ...
