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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1answer
32 views
Name of a state with $d-1$ excitations, distributed uniformly among $n$ qudits
Is there a particular name for a quantum state of the form (up to the normalization):
$$\sum_{i_1+\ldots+i_n = d-1} |i_1\rangle |i_2\rangle \ldots |i_n\rangle$$
or was it studied is some papers?
...
2
votes
1answer
90 views
Hermitian Adjoint of differential operator
I came across this equation (identity) (Eq. 4 in this paper):
$\int(-i d\psi/dx)^*\psi dx = \int \psi^*(-i d\psi/dx) dx + id(\psi^*\psi)/dx\mid_{-\infty}^{+\infty}$
I have trouble proving it. I ...
3
votes
2answers
73 views
Transfer of electron energy to atoms (heating up of matter by absorption of photons)
If an electron absorbs a photon to get exited to a higher energy level, it should either come back to same state or any other lower state by emitting the required photon. How then can there be a net ...
6
votes
1answer
177 views
Entangled or unentangled?
I got a little puzzled when thinking about two entangled fermions.
Say that we have a Hilbert space in which we have two fermionic orbitals $a$ and $b$. Then the Hilbert space $H$'s dimension is just ...
10
votes
3answers
224 views
The notion of an adiabatic process in thermodynamics -vs- quantum mechanics
I'm confused about the terminology in the two contexts since I can't figure out if they have a similar motivation. Afaik, the definitions state that quantum processes should be very slow to be called ...
1
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1answer
84 views
Finding the wavelength of an electron in its ground state?
To find the wavelength of an electron in its ground state in a hydrogen atom, would I or could I do the following?
Use the ground state energy (-13.6eV) in $E^2 = m^2c^4 + p^2c^2$
Solve for $p$
Use ...
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0answers
47 views
Finding the coefficients of a spinor
From the Schrödinger equation of a system I'm investigating, where the wave function is a 4-component spinor of coefficients $C_1, C_2, C_3, C_4$, I am able to obtain the expression
$\begin{pmatrix} ...
1
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1answer
40 views
Free 1d proton in magnetic field
Question Statement
Consider a proton which has spin $1/2$ that is free to move throughout all locations $-\infty<x<\infty$. A magnetic field of constant magnitude $B_{\circ}$ is applied ...
2
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3answers
105 views
When does the time independent Schrödinger equation have a physical solution?
In some cases, such as finite and infinite square wells, the Hamiltonian has energy eigenstates which correspond to physical wavefunctions.
In other cases, such as a one dimensional universe with ...
4
votes
3answers
106 views
Associating a Unitary operator to proper Lorentz transformations?
If one reads eg page 32 of Srednicki where he says:
In quantum theory, symmetries are represented by unitary (or
antiunitary) operators. This means that we associate a unitary
operator U(Λ) ...
-4
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0answers
37 views
Are we living inside a computer simulation is it true? [duplicate]
I am interested to know that are we living in computer simulation .
Help me to clear that with some samples ?
6
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0answers
110 views
Some questions about anyons?
(1) As we know, we have theories of second quantization for both bosons and fermions. That is, let $W_N$ be the $N$ identical particle Hilbert space of bosons or fermions, then the "many particle" ...
2
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0answers
61 views
Relativistic genarization of Quantum Harmonic Oscillator
I am trying to find out relativistic description of a quantum harmonic oscillator.
For a classical relativistic oscillator mass is a function of co-ordinates(http://arxiv.org/abs/1209.2876).
...
2
votes
1answer
80 views
Flux Quanta in the Arahanov-Bohm effect
I have been reading about the quantum hall effect during which i had to read about the AB effect used in the Laughlin gauge argument. In many sources, it is directly assumed that the flux quantum in ...
5
votes
0answers
238 views
Can the laws of quantum mechanics be derived from a more fundamental theory? [closed]
String theory takes quantum mechanics for granted and tries to make it compatible with gravity but if it turns out to be a theory of everything then shouldn't it in principle explain why our world is ...
4
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1answer
109 views
Quantum Mechanics - Hidden Variables
In Steven Weinberg's Lecture on Quantum Mechanics (p. 342), he writes:
The correlation between the spins of the two particles can be
expressed as the average value of the product of the ...
3
votes
1answer
73 views
Tunneling and transmission
Lets say we have a tunelling problem in the picture, where $W_p$ is a finite potential step:
If particle is comming from the left a general solutions to the Schrödinger equations for sepparate ...
4
votes
1answer
72 views
Simple uncertaintly calculation of the center coordinates of a Landau Level
I am reading the following review paper on the Quantum Hall Effect. I am sorry for the extremely stupid question, but I have been stuck on this very easy equation for long.
In equation 2.39, the ...
1
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1answer
89 views
Quantum computing and Pauli exclusion principle?
Ok so I saw this video by Brian Cox where he explains how no 2 particles can have same energy level.
Later I watched video "Was Brian Cox wrong?". Where they explained that he (probably on purpose) ...
2
votes
1answer
97 views
Energy density of a quantum mechanical ensemble
How do we determine the energy density of a given system? I have seen that the density operator
$$\rho~=~\frac{\exp(-\beta \hat{H})}{\text{tr}(\exp(-\beta \hat{H}))}.$$
What does this mean exactly ...
1
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1answer
64 views
Ground state energy of hydrogen molecule ion
In this paper, it is mentioned:
Furthermore, since the
energy of $H_2^+$in the ground state must be lower than that of an
H atom in the ground state,the negative (attractive) forces in the
...
1
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2answers
96 views
Is it only the spin of a particle that can be entangled with another particles spin?
Is it only the spin of a particle that can be entangled with another particles spin?
Also is there any good physical interpretation of the spin of a particle? because the rotational invariance of ...
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0answers
41 views
What is an example of a situation where Quantum Mechanics and Relativity do not work together? [duplicate]
I've learned special relativity in school last semester, and this semester we began learning about Quantum Mechanics, and my teacher told us that there was a Relativistic Schrodinger equation.
I was ...
2
votes
1answer
58 views
Quantum mechanical analogue of conjugate momentum
In classical mechanics, we define the concept of canonical momentum conjugate to a given generalised position coordinate. This quantity is the partial derivative of the Lagrangian of the system, with ...
1
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1answer
59 views
Calculation of the quantized Hall coefficient in the Integral Quantum Hall Effect
I have been reading about the QHE over the past couple of days. I am facing difficulty understanding a calculation in this review.
www.nimt.or.th/nimt/upload/linkfile/sys-metrology-248-434.pdf
In ...
3
votes
2answers
153 views
Why the K shell only contains 2 electrons?
It is written in my quantum physics book that the K shell contains only 2 electrons due to the Pauli principle.
I know that if $n = 1, l = 0, m = 0$, then the Hilbert space associated to the spin is ...
-5
votes
0answers
60 views
Consequences of Third Postulate of Special Relativity [closed]
Consequences of SR arise from two postulates.
know as this abstract states:
"relativistic action is limited to planck's constant", and maybe we've to consider it as the possible third postulate of ...
-1
votes
1answer
82 views
Operators in quantum mechanics
According to the Quantum Mechanics, can we write $\langle q|p\rangle = e^{ipq}$?
If so then how?
And if we transfer to integrate formulation then how it will look like?
2
votes
4answers
195 views
How do we know that there isn't a classical solution to the measurement problem/Quantum Mechanical uncertainty?
It was mentioned to me that it can be shown that there is no classical explanation for the uncertainty in Quantum Mechanics -- i.e. that there are no hidden workings that we have just not yet seen, ...
-1
votes
1answer
113 views
Double- well potential and Mexican potential
Is double well potential related to Maxican hat potential?
I have found on Quantum Field Theory in a Nutshell
by A. Zee
He wrote the double well potential as : $V (φ) = (λ/4)(φ^ 2 − v^2)^2$.
Can ...
1
vote
2answers
151 views
$\hbar \rightarrow 0$ in quantum mechanics
We often see a limit $\hbar \rightarrow 0$ in quantum mechanics and sometimes its related with Symmetry breaking. Can someone briefly write the story behind this limit.
Thanks in advance
3
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3answers
137 views
Does entropy alter the probability of independent events?
So I have taken an introductory level quantum physics and am currently taking an introductory level probability class. Then this simple scenario came up:
Given a fair coin that has been tossed 100 ...
4
votes
2answers
182 views
Why must the angular part of the Schrodinger Equation be an eigenfunction of L^2?
I was reading about the solution to the Schrodinger Equation in spherical coordinates with a radially symmetric potential, $V(r)$, and the book split the wavefunction into two parts: an angular part ...
1
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1answer
30 views
Electronic, vibrational and rotational autoionization
Can anyone please explain me the concept of electronic, vibrational and rotational autoionization.
What I understood is, autoionization usually occurs when the ion core is rotationally or ...
2
votes
0answers
84 views
Infinite degeneracy
Is something special for a quantum system with infinite degeneracy like free particle levels?
$E=\frac{\hbar^2 \vec{k}.\vec{k}}{2m}$
Edit: I mean what is physical (or mathematical) significance of ...
5
votes
1answer
87 views
Bremsstrahlung vs energy conservation
From Wikipedia:
Bremsstrahlung is electromagnetic radiation produced by the
deceleration of a charged particle when deflected by another charged
particle, typically an electron by an atomic ...
3
votes
1answer
209 views
How do I quantize a classical field theory
I have not been able to find any information about this on the Internet. I am a middle-schooler, 14, who self-studies physics, and I know up to and including ODEs, and some of the calculus of ...
1
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0answers
50 views
Helicity operator in Non relativistic limit
Helicity operator in Dirac equation is given by
$$H=\frac{\vec{S}\times \vec{P}}{P^{2}}$$
This operator commutes with dirac hamiltonian.We can also define a helicity(with same form) operator in case ...
3
votes
1answer
120 views
First order coherence function in terms of momentum distribution function
Can someone show me how the first order coherence function $G^1(r,r')\equiv \left \langle \hat{\Psi}(r)\hat{\Psi}(r') \right \rangle $ for a system of bosons is related to the momentum distribution ...
0
votes
0answers
27 views
Circuit identities HTH [closed]
Using this circuit indetities $HXH=Z, HYH=-Y, HZH = X$ prove $HTH=R_x(\pi/4)$. here $H$ is Hadamard matrix, $X,Y$ and $Z$ are Pauli matrix, $R_x$ is a rotation matrix and $T=\left[ \begin{array}{cc}
1 ...
5
votes
4answers
237 views
Physical Interpretation of the Integrand of the Feynman Path Integral
In quantum mechanics, we think of the Feynman Path Integral
$\int{D[x] e^{\frac{i}{\hbar}S}}$ (where $S$ is the classical action)
as a probability amplitude (propagator) for getting from $x_1$ to ...
2
votes
2answers
120 views
Vector representation of wavefunction in quantum mechanics?
I am new to quantum mechanics, and I just studied some parts of "wave mechanics" version of quantum mechanics. But I heard that wavefunction can be represented as vector in Hilbert space. In my eye, ...
2
votes
1answer
32 views
Probability Current in a time-varying scalar potential
I know that a vector potential has to be taken into account for the schrödinger probability current: $$\vec{j}=\frac{1}{2m} \left[ \Psi^*\hat{\vec{p}}\Psi-\Psi\hat{\vec{p}}\Psi^* - 2q\vec{A} |\Psi|^2 ...
5
votes
3answers
394 views
Does entanglement not immediately contradict the theory of special relativity?
Does entanglement not immediately contradict the theory of special relativity? Why are people still so convinced nothing can travel faster than light when we are perfectly aware of something that ...
1
vote
1answer
70 views
Uncertainty Principle and Energy range for an electron in an atom
I have the following exercise:
Use Heisenberg's uncertainty principle and the relation $\Delta u = \sqrt{\langle u^2 \rangle - \langle u \rangle^2}$ to find the range of energy an electron has in an ...
4
votes
0answers
101 views
Looking for modern results in semiclassical physics and relevant references
What are some important approximations, especially those that are state-of-the-art, used to approximate the many-body dynamics of atoms and molecules in the semiclassical regime? To be clear, I'm not ...
1
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0answers
26 views
Quantum graph theory: complex spectra
In quantum graph theory, what are the properties of a given graph to own complex conjugated complex eigenvalues, either finite or infinite? Spectral graph theory is as far as I know a not completely ...
4
votes
0answers
36 views
Relation of the Bloch-Siegert shift to the rotating pot lid
I see in Wikipedia that the Bloch-Siegert shift is analogies to the rotating pot lid, could you explain that analogy?
The Bloch-Siegert shift is a phenomenon in quantum physics that becomes ...
2
votes
0answers
40 views
Analytical solution of two level system driving by a sinusoidal potential beyond rotating wave approximation
A quantum mechanical two-level system driving by a constant sinusoidal external potential is very useful in varies areas of physics. Although the wildly used rotating-wave approximation(RWA) is very ...
4
votes
2answers
86 views
quantization of angular momentum
What is the most direct way of observation of quantization of angular momentum?
