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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20 views
Geometrical Representation Grover algorithm
I am study the Grover algorithm and in my lecture, and anothers lectures, exist this picture. My question is if the dimension of the computational basis is grather than 2 Why the evolution algorithm ...
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1answer
14 views
Why Quantum correlation is not uniform in this diagram?
Following diagram is from a Wikipedia article which shows Quantum Correlation for local hidden variables and Quantum Mechanics and experiments confirm Quantum Mechanics predictions.
My question is ...
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0answers
17 views
Is it possible to detect subjective decoherence? If yes, how?
In his paper from 1994 Thomas Breuer describes a phenomenon of subjective decoherence (p. 43). I wonder whether it can be measured, and if yes, how.
I also wonder whether it would allow to create an ...
5
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2answers
46 views
Is particle entanglement a binary property?
Is the particle entanglement a boolean property? That is, when we consider two given particles, is the answer to the question "are they entangled" always either "yes" or "no" (or, of course, "we are ...
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2answers
30 views
Using the Normalization Condition with Wavefunction
I'm very confused with this problem and I was looking for some guidance.
$$\psi(x) = Ae^{ikx}e^{-x^2/2a^2}$$
Use the normalization condition to find A.
So I understand that you use the normalization ...
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0answers
28 views
Can a link between photons that don't exist at the same time provide communication with the past?
They have published something about a link between photons that don't exist at the same time. Does this means that it is possible to build a device that will receive messages from itself but these ...
4
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2answers
66 views
How do you come up with a POVM?
This is a made-up example, just to understand a concept. If changing the probability values aids your explanation, that's fine by me.
Say you have a physical quantity $E$ that can take values 1, 2, 3 ...
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1answer
20 views
Frank Hertz experiment and different jumps
Why is it assumed that in this experiment, the jump will be between the second and the first states. Couldn't it be that when the electrons have enough energy, an atom absorbs enough to get to the ...
2
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1answer
43 views
Time evolution of a quantum state
I have another point in QM that I would like clarified. Suppose $$\{|n\rangle\}$$ is a set of eigenstates of both the Hamiltonian $H$ and another operator $\hat O$ corresponding to an observable also. ...
6
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1answer
67 views
Differential equation (Greens function) satisfied by the kernel using path integrals
How do I show that the kernel $K(x_2 t_2;x_1 t_1)=\int e^{\frac{i}{\hbar}S[2,1]}\mathcal{D}x$, satisfies the differential equation
$$-\frac{\hbar}{i}\frac{\partial K(2,1)}{\partial ...
2
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1answer
59 views
Can we apply de Broglie's relations to sound waves?
Can we apply the de Broglie relations to a sound waves ?
Is it possible?
if yes how do you do that?
what would be the mass(m) in the equation?
2
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2answers
30 views
Clarification on measurement in QM
Supppose we are given a quantum state that isn't pure state, such that it is a linear combination of the eigenstates of a Hermitian operator $\hat O$.
$$|\psi\rangle=N\sum \alpha_i |i\rangle$$ where ...
3
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1answer
60 views
Quantum Field Theory and Hilbert space dimensionality
Much (All?) of quantum theory can be done in separable Hilbert spaces with a countable basis.
How about quantum field theory? Is it “quite happy” (mathematically consistent) if everything is ...
2
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1answer
45 views
Hilbert space of a free particle: Countable or Uncountable?
This is obviously a follow on question to Hilbert space of harmonic oscillator: Countable vs uncountable?
So I thought that the Hilbert space of a bound electron is countable, but the Hilbert space ...
2
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1answer
59 views
Trying to understand mixed states
I took a basic quantum chemistry course (McQuarrie's "Quantum Chemistry"), but it never dealt with mixed states -- only pure states (or if it did, we never got to it in class).
So I'm trying to ...
23
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12answers
1k views
Quantum mechanics and everyday nature
Is there a phenomenon visible to the naked eye that requires quantum mechanics to be satisfactorily explained? I am looking for a sort of quantic Newtonian apple.
2
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0answers
25 views
How to numerically solve a laser driving semi-classical two-level system using Floquet formalism?
Consider the semi-classical laser driving two-level atom, where the laser is treated classically and the atom is treated quantum mechanically. The effect of laser on the atom is a dipole coupling:
$$
...
2
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2answers
70 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 ...
7
votes
1answer
90 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, ...
5
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2answers
66 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
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0answers
30 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 ...
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0answers
27 views
Finding Clebsh-Gordan coefficient [closed]
Two electrons , their angular quantum number =1 . Find the inner product of < 2 0 | 00 > ?
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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 &= ...
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1answer
39 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
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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 ...
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0answers
32 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
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1answer
106 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}$ ...
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0answers
53 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 ...
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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
47 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
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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 ...
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0answers
31 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.
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1answer
55 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
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2answers
90 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
31 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 ...
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0answers
22 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
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1answer
61 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
111 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
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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
41 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
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0answers
19 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
3answers
210 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 ...
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
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0answers
76 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
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2answers
59 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
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2answers
44 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) = ...
13
votes
3answers
199 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
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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
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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
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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 $\vec u$. ...
