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
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
146 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
634 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
48 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
93 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
52 views
The gauge-invariance of the probability current
It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\
\phi\to\phi-\frac{\partial \chi}{\partial t}\\
\psi\to \psi ...
1
vote
1answer
44 views
Energy eigenvalues of a Q.H.Oscillator with $[\hat{H},\hat{a}] = -\hbar \omega \hat{a}$ and $[\hat{H},\hat{a}^\dagger] = \hbar \omega \hat{a}^\dagger$
I just finished deriving the commutators:
\begin{align}
[\hat{H}, \hat{a}] &= -\hbar \omega \hat{a}\\
[\hat{H}, \hat{a}^\dagger] &= \hbar \omega \hat{a}^\dagger\\
\end{align}
On the ...
2
votes
2answers
79 views
Density Operator, Expectation Value, Coherent States
How would I go about evaluating expectation values like $\langle X \rangle$ and $\langle P \rangle$?
Work I've done:
I've done the integration over $\phi$ and rewrote $\rho$ as:
$\rho = ...
2
votes
1answer
38 views
State emitting from an extended thermal source
This calculation is for a double slit experiment setup which is experiencing a far field radiation from an extended monochromatic thermal source. I assume the source is 1-D and it's length is $b$. ...
2
votes
0answers
59 views
A general wavefunction in a square lattice
Suppose we have a square lattice with periodic condition in both $x$ and $y$ direction with four atoms per unit cell, the configuration of the four atoms has $C_4$ symmetry. What will be a general ...
3
votes
2answers
183 views
Coherent State, Unitary Operators, Harmonic Oscillator
Consider the operator:
$$O = e^{\theta(a^\dagger b - b^\dagger a)}$$
where $\theta$ is a constant.
$O$ is a unitary operator.
$a$, $a^\dagger$, $b$, and $b^\dagger$ are ladder operators for two ...
1
vote
1answer
82 views
Could the shadow move with faster-than-light speed? [duplicate]
If I make a huge laser with a figure for shadow in front of the laser, and I shine it on to the moon, will I see the light from the laser AND the shadow moving the same speed? (I read somewhere the ...
3
votes
0answers
23 views
Energy needed to raise energy level of an atom? [duplicate]
Suppose I have an atom at rest which is at energy level $E_i$. Would it be possible to raise it to the next higher level $E_{i+1}$ by shooting a photon of energy $E_{i+1}-E_i$ at it?
I ask because ...
1
vote
1answer
51 views
Eigenfunctions in a harmonic oscillator
This assignment is about the one dimensional harmonic oscillator (HO).
The hamiltonian is just as you know from the HO, same goes for the energies, but I get that the wavefunction of the particle, at ...
7
votes
1answer
105 views
How are qubits better than classical bit?
WHAT I KNOW:
classical computers store information in bits which can either be 0 or 1, but in quantum computer the qubit can store 0 , 1 or a state that is the superposition of these two states.
Now ...
0
votes
1answer
77 views
QED photon propagator to one-loop order gets different answers
I'm a self-studying 14-year-old who has a passion for particle physics. I'm currently trying to calculate the QED photon propagator to one loop. However, in all the places I've looked, even with the ...
1
vote
0answers
26 views
Non reciprocal light propagation
In search for some explanation in why magneto-optical materials (like the one used in the Faraday rotator and, consequently, in the "optical diode") act in such a "strange" way, I saw that this kind ...
3
votes
1answer
120 views
Phase space in quantum mechanics and Heisenberg uncertainty principle
In my book about quantum mechanics they give a derivation that for one particle an area of $h$ in $2D$ phase space contains exactly one quantum mechanical state.
In my book about statistical physics ...
2
votes
1answer
61 views
Time evolution operator to find expectation value
I have a state $\Psi (x,0) = \sum_{n=0}^{\infty} c_{n}u_n(x)$ and want to find the expectation value of any observable A at time t, $\langle \Psi(t)|\hat{A}|\Psi(t)\rangle$.
I know that I should ...
3
votes
5answers
138 views
What counts as “observation” in Schrödinger's Cat, and why are superpositions possible?
So if I understood correctly, Schrödinger's Cat is a thought experiment that puts a cat inside a box, and there's a mechanism that kills the cat with 50% probability based on a quantum process. The ...
7
votes
7answers
363 views
Why Quantum Mechanics as a non-fundamental effective theory?
My question: What (physical or mathematical) reasons (not philosophical) do some physicists ('t Hooft, Penrose, Smolin,...) argue/have in order to think that Quantum Mechanics could be substituted by ...
1
vote
1answer
50 views
Casimir force using Pauli-Villars regularization
In Zee's Quantum field theory in a nutshell, 2nd edition, p. 74 he claims that:
$$
\sum_a c_a \Lambda_a \sum_n \frac{\omega_n}{\omega_n + \Lambda_a} = - \sum_a c_a \Lambda_a \sum_n ...
4
votes
2answers
85 views
Independent systems and Lagrangians
Definition 1:
The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
4
votes
2answers
90 views
Proof for commutator relation $[\hat{H},\hat{a}] = - \hbar \omega \hat{a}$
I know how to derive below equations found on wikipedia and have done it myselt too:
\begin{align}
\hat{H} &= \hbar \omega \left(\hat{a}^\dagger\hat{a} + \frac{1}{2}\right)\\
\hat{H} &= ...
0
votes
1answer
52 views
Where is the amplitude of electromagnetic waves in the equation of energy of e/m waves?
Does the amplitude of the photon oscillations always stay constant and if it is not - what are the physical differences between the photon with higher amplitude in comparison to the one with the less ...
3
votes
3answers
98 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
85 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
56 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
votes
1answer
53 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
votes
2answers
146 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 ...
0
votes
1answer
45 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
votes
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
113 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
votes
0answers
112 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
votes
0answers
31 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
votes
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
votes
1answer
59 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
146 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
83 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
votes
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}}$$
What is the corresponding point on the extended complex plane and Bloch sphere?
How to perform calculations and get the point representing ...
0
votes
1answer
36 views
Time Dependent HydroHow would I go about writing the time dependent wave function given the wavefunction at $t=0$? gen Wave Function
1) How vwoulHow would I go about writing the time dependent wave function given the wavefunction at $t=0$?
go about writing the time dependent wave function given the wavefunction at $t=0$?
...
3
votes
2answers
191 views
QM formalism is one big confusion - lack of geometrical explaination with images
I have been trying to learn QM and it went well (all untill harmonic oscilator) until i had to face the formalism:
Hilbert space- As a novice to QM i am very sad that in none of the books i have ...
2
votes
3answers
94 views
How do I determine the location of a free particle with Schrödinger's equation?
I'm trying to get to grips with the Schrödinger equation by looking at a free particle. I'm certain at some point I massively misunderstood something.
According to a textbook and a lecture the free ...
4
votes
2answers
73 views
Translator Operator
In Modern Quantum Mechanics by Sakurai, at page 46 while deriving commutator of translator operator with position operator, he uses $$\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 ...
