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 ...
2
votes
2answers
22 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
1answer
32 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
26 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 ...
12
votes
2answers
91 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
34 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
0answers
72 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
66 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
51 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
38 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
$$\psi(x,0) = ...
11
votes
3answers
139 views
Hilbert space of harmonic oscillator: Countable vs uncountable?
Hm, this just occurred to me while answering another question:
If I write the Hamiltonian for a harmonic oscillator as
$$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$
then wouldn't one set of ...
0
votes
0answers
36 views
Question regarding operators and cylindrical coordinates
I have the following problem in my hand:
I need to arrive from the Cartesian expression $$x_{j}{\partial_{k}}x_{j}{\partial_{k}}-x_{j}{\partial_{k}}x_{k}{\partial_{j}}$$
to this expression:
...
0
votes
0answers
19 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
80 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
23 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
68 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 ...
-2
votes
0answers
56 views
How can superstring theories unify general relativity and quantum theory when no prediction can be made?
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
64 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
90 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
114 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
60 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
59 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
41 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
84 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
56 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
231 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 ...
0
votes
2answers
51 views
Electron in an infinite potential well
Does this problem have any sense?
Suppose an electron in an infinite well of length $0.5nm$. The state of the system is the superposition of the ground state and the first excited state. Find the ...
3
votes
1answer
77 views
Motivation for Wigner Phase Space Distribution
Most sources say that Wigner distribution acts like a joint phase-space distribution in quantum mechanics and this is justified by the formula
...
6
votes
3answers
205 views
Why is the Dirac equation not used for calculations?
From what I understand the Dirac equation is supposed to be an improvement on the Schrödinger equation in that it is consistent with relativity theory. Yet all methods I have encountered for doing ...
0
votes
0answers
18 views
Degeneracy of orbitals in magenetic field
Why is that in an external magnetic field(uniform) the degeneracy of d,f orbitals is lost but the degeneracy of p orbitals remain intact assuming the main cause of losing degeneracy is the difference ...
1
vote
3answers
106 views
Complex energy eigenstates of the harmonic oscillator
Given the Hamiltonian for the the harmonic oscillator (HO) as
$$
\hat H=\frac{\hat P^2}{2m}+\frac{m}{2}\omega^2\hat x^2\,,
$$
the Schroedinger equation can be reduced to:
$$
\left[
...
1
vote
2answers
113 views
$\langle B|A \rangle$ expressed in terms of the Partition Function
Say you have an electron departing from point A and reaching poing B after a time t.
According to some helping friend, the Partition Function for that electron going from point A to B can be written ...
1
vote
1answer
172 views
Which is this formula Feynman talks about in the QED book?
I am reading the fantastic QED Feynman book. He talks in chapter 3 about a formula he considers too complicated to be written in the book. I would like to know which formula he talks about, although I ...
6
votes
1answer
83 views
What experiments have been proposed to discriminate between interpretations of quantum mechanics?
There are a lot of potentially correct interpretations of quantum mechanics. While I've heard descriptions of a lot of them, I've never heard of an experiment being done to test any of them aside from ...
1
vote
2answers
78 views
Are there problems solvable with Newtonian physics, GR and QM?
First I must let you know that I don't have much understanding of neither GR nor quantum mechanics, and therefore this question.
I've mentally pictured Newtonian physics, GR and quantum mechanics all ...
3
votes
1answer
82 views
Field operator eigenvalues
For an harmonic oscillator we can write the Hamiltonian eigenvalues in the basis of the amplitude eigenvalues : for example the ground state is a gaussian : $⟨x|0⟩=a.e^{-b.x^{2}}$.
I was wondering ...
2
votes
2answers
107 views
How do we know that $\psi$ is the eigenfunction of an operator $\hat{H}$ with eigenvalue $W$?
I am kind of new to this eigenvalue, eigenfunction and operator things, but I have come across this quote many times:
$\psi$ is the eigenfunction of an operator $\hat{H}$ with eigenvalue
$W$.
...
1
vote
1answer
45 views
Is the de Broglie wavelength of a photon equal to the EM wavelength of the radiation?
Is the de Broglie (matter) wavelength $\lambda=\frac{h}{p}$ of a photon equal to the electromagnetic wavelength of the radiation?
I guess yes, but how come that photons have both a matter wave and an ...
0
votes
1answer
41 views
Why doesn't intensity of light affect the emission of electrons?
So electrons of specific atoms have a minimum amount of energy needed to escape the atom, called the work function, W. Now let's say that you emit a certain frequency of light, and $hf<W$. However, ...
2
votes
0answers
75 views
Topological band theory [closed]
Why topological insulators were discovered so late? While the band theory was known long time ago! I mean why the topological properties of electronic bands were not noticed in the past?
2
votes
1answer
46 views
Possible states for two electrons in the helium atom
Consider the helium atom with two electrons, but ignore coupling of angular momenta, relativistic effects, etc.
The spin state of the system is a combination of the triplet states and the singlet ...
1
vote
1answer
37 views
localized electrons in the crystals
Why electrons in low lying levels of individual atoms stay localized in their own atoms in a crystal? Doesn't this contradict Bloch's theorem?
1
vote
2answers
143 views
Where does quantum mechanics come from? [closed]
Where does quantum mechanics come from?
If string theory is proved to be the correct quantum theory of gravity but it failed to explain where quantum mechanics came from can we still consider it a ...
12
votes
3answers
587 views
Is the universe fundamentally deterministic?
I'm not sure if this is the right place to ask this question. I realise that this maybe a borderline philosophical question at this point in time, therefore feel free to close this question if you ...
1
vote
0answers
49 views
Studying QM without math and physics background [duplicate]
I rode all posted answers about this topic but i need to ask you another information. I have done a semester course called "Principle of Physics" (i am studying Biotechnology) and one called ...
-1
votes
0answers
46 views
What is the difference between various fields of physics? [closed]
what is the difference between the fields of physics? like high energy physics, particle physics, cosmology, quantum physics, quantum mechanics, experimental physics, theoretical physics, applied ...
7
votes
1answer
92 views
Positivity in the Pauli/Bloch/coherence vector representation
Suppose $\rho$ is an $n$-qubit state and $\vec{x}$ is a vector of coefficients in the Pauli representation (also called the Bloch or coherence vector). That is
$$
x_k = {\rm Tr}(\rho \sigma_k),
$$
...
0
votes
0answers
51 views
The gauge-invariance of the probability current
It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\
\phi\to\phi-\frac{\partial \chi}{\partial t}\\
\psi\to \psi ...
