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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99 views
Reaching the speed of light via quantum mechanical uncertainty?
Suppose you accelerate a body to very near the speed of light $c$ where $v = c - \epsilon$. Although this would take an enormous energy, is it possible the last arbitrarily small velocity needed -- ...
4
votes
2answers
87 views
Do we always ignore zero energy solutions to the (one dimensional) Schrödinger equation?
When we solve the Schrödinger equation on an infinite domain with a given potential $U$, much of the time the lowest possible energy for a solution corresponds to a non-zero energy. For example, for ...
2
votes
1answer
57 views
Difference between vector and pseudo-scalar
In physics, a pseudo-scalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as improper rotations while a true scalar does not.
Can someone show me ...
2
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1answer
54 views
The matrix element of a normal-ordered operator
Eq (1.137) in Negele and Orland gives the following identity for a normal-ordered operator $A(a_i^\dagger,a_i)$:
$$\langle \phi|A(a_i^\dagger,a_i)|\phi'\rangle=A(\phi_i^*,\phi'_i)e^{\sum ...
2
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2answers
148 views
In quantum mechanics(QM), can we define a high-dimensional “spin” angular momentum other than the ordinary 3D one?
Inspired by my previous question Questions about angular momentum and 3-dimensional(3D) space? and another relevant question How to define angular momentum in other than three dimensions? , now I get ...
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1answer
46 views
EM Waves Energy Loss
Where does the energy go when two photons interfere destructively at a point on a screen in Young's double slit experiment ?
2
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2answers
64 views
Hamiltonian of Harmonic Oscillator with Spin Term
We have the usual Hamiltonian for the 1D Harmonic Oscillator:
$\hat{H_{0}}=\frac{\hat{P^2}}{2m} + \frac{1}{2}m \omega \hat{X^2}$
Now a new term has been added to the Hamiltonian, $\hat{H} = ...
8
votes
1answer
117 views
What're the relations and differences between slave-fermion and slave-boson formalism?
As we know, in condensed matter theory, especially in dealing with strongly correlated systems, physicists have constructed various "peculiar" slave-fermion and slave-boson theories. For example,
For ...
3
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0answers
115 views
projective measurement & POVM
Let us consider the following completely positive map $\mathcal{B}(\mathbb{C}^n)\ni\rho\mapsto L\rho L^\dagger$, where $L\in\mathcal{B}(\mathbb{C}^n)$ is any arbitrary operator (and can have rank ...
0
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0answers
32 views
Physical significance of effective wave function
In Yanhua Shih's book on quantum optics, the coherence functions are expressed in terms of effective wave function. Here are the expressions for single photon wave packets.
To derive the coherence ...
4
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2answers
145 views
Integer physics
Are there interesting (aspects of) problems in modern physics that can be expressed solely in terms of integer numbers? Bonus points for quantum mechanics.
2
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1answer
62 views
Dark and bright areas around atoms in a scanning tunnelling microscope image
Recently IBM created world’s smallest ever animation on an atomic scale video. Researchers made the animation using a scanning tunnelling microscope to move thousands of carbon monoxide molecules to ...
3
votes
2answers
150 views
Determinism, classical probabilities, and/or quantum mechanics?
[I]f you want a universe with certain very generic properties, you seem forced to one of three choices: (1) determinism, (2) classical probabilities, or (3) quantum mechanics. [My emphasis.]
...
3
votes
0answers
85 views
$U(N)$ gauged quantum mechanics
I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic?
The action I am interested in is
...
0
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0answers
38 views
Deutsch-Jozsa algorithm [closed]
How many calls are required to determine is the function balanced or not on the classical computer with probability of error < 50%.
Ref: Deutsch-Jozsa algorithm.
2
votes
0answers
50 views
Standard Quantum Mechanics representation as a constrained 2 + 1 space-time (membrane) theory?
Could a particular Standard Quantum Mechanics representation be a constrained 2 + 1 space-time theory (membrane theory) ?
(i) This question is motivated by a possible (approximative) analogy with ...
1
vote
2answers
63 views
Qubit projections
Given the qubit:
$$\frac{|0\rangle+i|1\rangle}{\sqrt{2}}$$
What is the corresponding point on the extended complex plane and Bloch sphere?
How to perform calculations and get the point representing ...
0
votes
1answer
41 views
Time Dependent HydroHow would I go about writing the time dependent wave function given the wavefunction at $t=0$? gen Wave Function
1) How vwoulHow would I go about writing the time dependent wave function given the wavefunction at $t=0$?
go about writing the time dependent wave function given the wavefunction at $t=0$?
...
3
votes
2answers
196 views
QM formalism is one big confusion - lack of geometrical explaination with images
I have been trying to learn QM and it went well (all untill harmonic oscilator) until i had to face the formalism:
Hilbert space- As a novice to QM i am very sad that in none of the books i have ...
2
votes
3answers
96 views
How do I determine the location of a free particle with Schrödinger's equation?
I'm trying to get to grips with the Schrödinger equation by looking at a free particle. I'm certain at some point I massively misunderstood something.
According to a textbook and a lecture the free ...
4
votes
2answers
74 views
Translator Operator
In Modern Quantum Mechanics by Sakurai, at page 46 while deriving commutator of translator operator with position operator, he uses $$\left| x+dx\right\rangle \simeq \left| x \right\rangle.$$ But for ...
2
votes
1answer
62 views
Moyal Product in Non Commutative Quantum Mechanics
Can someone please explain me what is a Moyal product?
Also, how does putting $$X_a(\psi) ~=~ x_a\star\psi$$ realise $$[X_a,X_b]=i\theta_{ab}{\bf 1}?$$
Ref: Quantum mechanics on non-commutative ...
2
votes
1answer
51 views
Why does the quantum eraser seem to violate energy and momentum conservation?
In the literature of the quantum eraser experiment it is argued that the change in statistics of the system from non-interference to interference is due to the erasing of "distinguishing information". ...
0
votes
1answer
59 views
Two qubits problem [closed]
Given the 2 qubit state:
(a/b) |00> + (c/b) |01> + (c/b) |10> + (d/b) |11>
What is the probability that 2 qubits are equal?
Thanks much!
1
vote
1answer
74 views
Mathematical explanation of quantum teleportation
I am now studying quantum teleportation. I get what the process is like but I'm wondering why it happens this way.
You've got two entangled particles A and B whose wavefunctions are entangled. You ...
0
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0answers
44 views
Constructing a Toffoli gate from CNOT and single-qubit gates [closed]
Toffoli gate in terms of CNOT and single-qubit gates.
Thanks much!
1
vote
0answers
33 views
What is the difference between Cramer and Vaidman?
Two very interesting new papers on arXiv last night by Lev Vaidman and friends lead me to ask about the differences between Cramer's transactional interpretation of quantum mechanics (TIQM) and the ...
0
votes
0answers
21 views
What does it mean to erase the which-path information of something?
In this particular case, I am told that very fast measurements erase which-path frequency information of photons.
I'm not really sure what that means though. I do not entirely understand the concept ...
6
votes
1answer
182 views
Can a photon exhibit multiple frequencies?
Can a photon be a superposition of multiple frequency states? Kind of similar to how an electron can be a superposition of multiple spin states.
2
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2answers
123 views
How is the hamiltonian a hermitian operator?
My book about quantum mechanics states that the hamiltonian, defined as $H=i\hbar\frac{\partial}{\partial t}$ is a hermitian operator. But i don't really see how I have to interpret this. First of ...
0
votes
0answers
62 views
What does this notation mean in terms of quantic numbers, and how to imagine the electrons in this quantic system? (Helium $2^1$ $P$ and $2^3$ $P$)
Helium atom in the $2^1$ $P$ and $2^3$ $P$ excited states
Now I'm guessing that 1 electron should be considered in the 1s state, but what about the other?
Should I consider the other as simply ...
-1
votes
1answer
45 views
Heisenberg's uncertainty and $0 K$ temperature
when a body is subjected to $0 K$ temperature, it becomes rigid. hence if we see in terms of quantum the lattice vibration decreases, resulting in no change in the direction of the Random velocity, ...
3
votes
1answer
138 views
Schrödinger equation for a harmonic oscillator
I have came across this equation for quantum harmonic oscillator
$$
W \psi = - \frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + \frac{1}{2} m \omega^2 x^2 \psi
$$
which is often remodelled by defining a new ...
-3
votes
0answers
37 views
How to calculate the discord of a given quantum state? [closed]
I want to calculate the discord of a given two-qubit state $\rho$ by Mathematica but can not find a '.m' file to make this process easy. The only thing I can do is to calculate it step by step by ...
0
votes
1answer
58 views
What is inner product of the vacuum state with itself?
If $|0 \rangle$ is the vacuum state in quantum mechanics and $\alpha$ is any complex number, what is $\langle 0 | \alpha | 0 \rangle$? I need to have that $\langle 0 | \alpha | 0 \rangle = \alpha$, ...
0
votes
1answer
84 views
Matrix representation for fermionic annihilation operator
My guess it should look something like this:
$ c_\sigma = ...
1
vote
0answers
22 views
Laughlin state unique ground state?
In the FQHE, one typically encounters the statement that the $\nu = 1/3$ Laughlin state is a unique exact ground state of a model Hamiltonian where the Haldane pseudopotentials $V_1 \neq 0$ and $V_m = ...
0
votes
0answers
34 views
Quantum harmonic oscilator - book that does it all right [duplicate]
I am dealing with quantum harmonic oscillator.
In every single book or video i have checked out i can read how the mathematical technique for solving this Schrödinger equation:
$$
W\psi = - ...
1
vote
1answer
63 views
Is Dirac's description of a photon in a split beam still seen as correct today?
This comes from the Interference of Photons section in the book The Principles of Quantum Mechanics by P Dirac:
We shall discuss the description which quantum mechanics provides of the ...
5
votes
2answers
146 views
De Broglie wavelength, frequency and velocity - interpretation
Two fundamental equations regarding wave-particle duality are:
$$ \lambda = \frac{h}{p},
\\
\nu = E/h .$$
We talk about de Broglie wavelength, is it meaningful to talk about de Broglie frequency ...
2
votes
0answers
32 views
Perturbation in Supersymmetric Quantum Mechanics.
To do perturbation analysis of Supersymmetric Quantum Mechanical Hamiltonian, the superpotential is first scaled by a constant $\lambda >> 1$ and then expanded about it's critical point. Finally ...
0
votes
2answers
69 views
Purpose of Grover's algorithm?
How is the output of Grover's algorithm useful if the result is required to use the oracle? If we already know the desired state, what's the point of using the algorithm?
-1
votes
2answers
144 views
Quantum tunneling is faster than light travel?
Quantum tunneling is faster than light travel ?
My reasoning is that the particle cannot be detected inside the tunnel so if it travels from A to B it must be instantly going from A to B , hence ...
1
vote
1answer
97 views
Discretization of action in path integral
I am reading Peskin and Schroeder (path integrals) and it states that discretising the classical action gives:
$$S~=~\int \left(\frac{m}{2}\dot{x}^{2}-V(x)\right)
dt ~\rightarrow~ \sum ...
0
votes
0answers
54 views
Hamiltonian matrix propertu
A professor made an statement to prove the variational theorem:
Because the Hamiltonian (H operator of quantum physics) is diagonal in its own eigenfunction, the terms in $\left \langle \Phi _{m} ...
0
votes
1answer
32 views
Violation of the Normalization Constraint?
Say we have two qubits $|a\rangle$ and $|b\rangle$ both initialized to $|0\rangle$. We then apply the rotation gate $R_{x}(\frac{\pi}{2})$ of matrix representation
$\left( \begin{array}{}
...
2
votes
1answer
105 views
Questions about angular momentum and 3-dimensional(3D) space?
Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
3
votes
2answers
116 views
Quantum commutator
I'm given this commutator:
$$\left[PXP,P\right]$$
Being $P\psi=-i\hbar\partial_x\psi$, and $X\psi=x\psi$
I've solved it in two ways, the first one is just aplying the commutator to some function ...
0
votes
1answer
113 views
is really an atom stable?
Half filled and fulfilled atomic orbitals are stable because of :
high exchange energy.
The problem is with exchange energy. We have learnt that the half and fulfilled orbitals have maximum no. of ...
0
votes
3answers
130 views
Can an electron interact with itself to create interference?
I have been recently brushing up my elementary physics concepts, specifically quantum physics. So, if I set up a single photon emitter in the double slit experiment, it is possible for me to see ...
