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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What is the actual significance of the amplituhedron?

The news that physicists have discovered a geometrical object that simplifies a lot our models of quantum physics has recently became viral. For an outsider like me, it is difficult to actually ...
11
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2answers
752 views

In what sense is the path integral an independent formulation of Quantum Mechanics/Field Theory?

We are all familiar with the version of Quantum Mechanics based on state space, operators, Schrodinger equation etc. This allows us to successfully compute relevant physical quantities such as ...
2
votes
1answer
112 views

Coefficients of the vectors in a tensor product

The postulate says that if we want to build the compound state of two sub-systems, we just take the tensor product $\otimes$ of the respective state vectors. This means that if one of the vectors has ...
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vote
1answer
188 views

What's the relationship between the energy density of a black-body and its radiant exitance?

Through a bit calculation we can derive that in a cavity, the energy density $$u(f,T)=\overline{E(f)}\times G(f)=\frac{8\pi h}{c^3}\frac{f^3}{e^{h\nu /kT}-1}$$ If we take the integral over all ...
0
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2answers
1k views

Quantum mechanics potential barrier problem [duplicate]

While reviewing some quantum mechanics, I cam across a very interesting situation. For a potential barrier, if a particle has an energy $E$ less than the potential barrier $V_0$, it is possible to ...
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3answers
453 views

$\mathrm{Tr}(XY) = \mathrm{Tr}(YX)$?

I'm trying to understand the Dirac notation to understand quantum mechanics better. I'm trying to show the above relation using the Dirac notation. Given $$\mathrm{Tr}(X)~=~\sum_j\langle ...
0
votes
0answers
142 views

What the quantum spin refers to? How we calculate the angular momentum $\omega$ from the spin quantum number?

How we calculate the angular momentum $\omega$ from the spin quantum number, to know how fast a particle rotating on its own axis?
1
vote
1answer
2k views

Energy and probability for the particle in a box

The question statement: we have a particle of mass m in a box of length a. The wavefunction is given as $$\psi(x)=x\sin \left(\frac{\pi x}{a}\right)$$ It asks to normalize the wave function and find ...
0
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0answers
56 views

The electron and classical dynamics

Can I use Newtonian laws of dynamics and kinematics applied to electrons (like $F = ma$ and $s = s_0 + v_0 t + at^2/2$)? If not, why not? I know that everything in principle behaves in a quantum ...
6
votes
3answers
5k views

What is coherence in quantum mechanics?

What are coherence and quantum entanglement? Does it mean that two particles are the same? I read this in a book called Physics of the Impossible by Michio Kaku. He says that two particles behave in ...
2
votes
1answer
101 views

Positive cone of operators: if two selfadjoints $a$, $b$ obey $a^2 + b^2 =1$, must they commute?

The question relates to the structure of the positive cone of operators, in C*-algebra. If $a$ and $b$ are selfadjoints such that $a^2 + b^2 = 1$ can one prove $a$ and $b$ commute? What one ...
0
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2answers
3k views

Expectation Values in Quantum Mechanics

Why is the expectation value what it is? Why don't you apply the operator, then multiply that by it's conjugate?
2
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2answers
6k views

What is the Momentum Operator?

I know the equation for the momentum operator, but what exactly is the momentum operator? It's bizarre to me that taking the derivative of the wave function, which is an operator, should return ...
1
vote
2answers
192 views

A machine which copies any object with 100% accuracy?

Does physics allow for a machine that copies an object with 100% accuracy?
4
votes
3answers
2k views

Fermionic anti-commutation relations

For Pauli's exclusion principle to be followed by fermions, we need these anti-commutators $$[a_{\lambda},a_{\lambda}]_+=0 $$ and $$[a_{\lambda}^{\dagger},a_{\lambda}^{\dagger}]_+=0 $$ Then ...
4
votes
2answers
978 views

Need help understanding Semiconductor physics

I am trying to read Kittel for a project, and he mentions the properties on silicon and germanium so briefly, that I don't understand it at all. He talks about p states, and I don't really know what ...
1
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2answers
451 views

Complex Versus Real Wave Velocities in Quantum Mechanics

There's a fantastic quote in Schrodinger's second 1926 paper1 that apparently provides some motivation for the discrete energy levels (I think) that I'm having trouble interpreting: I would not ...
2
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0answers
129 views

How to name different approaches to relativistic quantum theory

In the introductory chapter of the QFT book by Mark Srednicki the author notes that [p. 26] So now we have two different approaches to relativistic quantum theory [...] Which [one of those two] we ...
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0answers
50 views

How to prove Newton's second law with quantum mechanics? [duplicate]

Newton's second law claims that $F=ma$. In terms of quantum mechanics, the equality can be written as $ \frac{d\langle p \rangle}{dt} = -\langle \nabla V(x) \rangle$. How can I prove this with ...
3
votes
1answer
593 views

Non-relativistic limit of complex scalar field

In page 42 of David Tong's lectures on Quantum Field Theory, he says that one can also derive the Schrödinger Lagrangian by taking the non-relativistic limit of the (complex?) scalar field Lagrangian. ...
15
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3answers
5k views

Why do we use operators in quantum mechanics?

In classical mechanics, physical quantities, such as, e.g. the coordinates of position, velocity, momentum, energy, etc, are real numbers, but in quantum mechanics they become operators. Why is this ...
8
votes
1answer
570 views

How does entanglement work independent of time?

A recent experiment shows that it is possible to entangle two particles that never co-existed in time. Time line diagram. (I) Birth of photons 1 and 2, (II) detection of photon 1, (III) birth of ...
3
votes
2answers
332 views

Thermalisation - Open quantum systems

I would like to understand better a phenomenon of a quantum heat bath. Below I present one example, which seems quite clear to me. It would be great to see some less-discrete models, and more ...
8
votes
2answers
2k views

Why can't I just think the spin as rotating?

I'm going mad about the problem. I really don't understand why do electron have 1/2 spin number, why they are not actually spinning. I can accept that the electrons have their own magnetic field, ...
2
votes
0answers
127 views

Is time ordering defined for a single operator depending of two time variables?

The time ordering for the purpose of quantum mechanics is e.g. given by $${\mathcal T} \left[A(x) B(y)\right] := \begin{matrix} A(x) B(y) & \textrm{ if } & x_0 > y_0 \\ \pm B(y)A(x) & ...
5
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1answer
131 views

Visualizing irreps of SU(N)

What physical system can one use as an example while considering irreps of SU(N)? What is the correspondence between the system and the irreps?
3
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0answers
123 views

Optimality of product input state in quantum channel

Let $\mathcal N^{A_1\rightarrow B_1}_1,..,\mathcal N^{A_1\rightarrow B_1}_k$ be a set of valid quantum evolutions with equal input and output dimensions. And let the effect of a channel on a system ...
7
votes
2answers
588 views

“Correlation energy” using the pair correlation function

In this paper on the Quantum Hall effect the authors refer to something called the correlation energy of electrons. It is defined at the top of page 5 as $E=\frac{n}{2}\int (g(r)-1)V(r)dA\ ,$ where ...
18
votes
2answers
2k views

What is the difference between the Balmer series of hydrogen and deuterium?

In my quantum mechanics textbook, it claims that the Balmer series between hydrogen and deuterium is different. However, I was under the impression that the Balmer series $$H_\alpha, H_\beta, ...
4
votes
3answers
244 views

Quantum circuit equivalent of quantum pseudo-telepathy game

I'm trying to understand the wikipedia article on quantum pseudotelepathy. I've been trying to figure out the quantum circuits the players can use to win the game from the wiki article. (Level of ...
2
votes
1answer
124 views

Is continuous evolution from one eigenstate of operator $O$ to another $O$-eigenstate possible?

Eigenvectors associated with distinct values of an observable are orthogonal, according to quantum mechanics. Does this entail that a quantum system cannot continuously evolve from one eigenstate ...
3
votes
2answers
326 views

Quantum Mechanical Meaning of Atomic Orbitals

According to quantum mechanics, for multi-electron atoms, a single electron around the nuclei can be in the state of linear combination of different eigen energy states. In that case, even the energy ...
12
votes
6answers
1k views

What is Quantization?

In classical mechanics you construct an action (involving a Lagrangian in arbitrary generalized coordinates, a Hamiltonian in canonical coordinates [to make your EOM more "convenient & ...
1
vote
1answer
205 views

About Pauli-Lubanski 4-vector

I saw you answered someone else about the Pauli-Lubanski 4-vector properties. I was doing some simple analysis of polarized leptons, started with the canonical convention of the spin operator wich is ...
2
votes
1answer
623 views

Volume charge density of H-atom

I have a problem where I am supposed to calculate the volume charge density of a neutral hydrogen atom. The potential is given to be $$ \Phi = k \frac{e^{-ar}}{r} \left(1 + \frac{ar}{2}\right) $$ Now ...
2
votes
1answer
181 views

Has Bell really demonstrated that no local hidden variable theory can exist in his original paper of 1964? Why then verify the CHSH violation?

The more I read about it and the more I'm convinced I haven't understood what I thought I had. In the original paper ...
0
votes
0answers
229 views

Is the Copenhagen interpretation still valid?

"The secret lives of photons revealed" - physicsworld.com. It seems that this experiment violates the Copenhagen interpretation. Is it still valid? Can you please give me more insight on this ...
6
votes
3answers
554 views

Uncertainty principle and the energy-momentum 4-vector

In each of the uncertainty relations $$\Delta p_x \Delta x \geq \hbar/2$$ $$\Delta p_y \Delta y \geq \hbar/2$$$$\Delta p_z \Delta z \geq \hbar/2$$$$\Delta E \Delta t \geq \hbar/2$$ the second term on ...
4
votes
6answers
634 views

Fermion vs. Bosons and particle vs. wave: is there a link?

I'm puzzled since several years on this basic aspect of quantum mechanics. Quantum theory is supposed to describe particle-wave symmetry of our world. It also describes our universe in term of bosons ...
2
votes
2answers
1k views

Are random quantum phenomena happening without a cause?

In everyday life, most of us assumes every event and object has a cause in some sense. I am wondering if the same is true for quantum physics. Does the random nature of quantum phenomena mean they ...
8
votes
2answers
417 views

Quantum states as rays as opposed to vectors

I recently read that a quantum state is actually defined by a ray and not a vector. That is it is possible to multiply a state $\psi$ by any complex number $c\in \mathbb{C}$ and you won't be changing ...
1
vote
1answer
141 views

Four vector manipulation

I have started doing Relativistic Quantum Mechanics from Greiner. I'm having difficulty understanding the following derivation for commutation relations (page 4): $$[\hat{p}^\mu, x^\nu] = ...
0
votes
1answer
957 views

Covariance of the Dirac equation and Infinitesimal Lorentz transformation

Okay, I've got really desperate now. I've spend 10 hours of work (for a few days) trying to prove 'trivial' equation in Quantum Electrodynamics. To anybody who want to write an answer for my questions ...
0
votes
1answer
160 views

Explicit solutions to 2-d Dirac Equation

The 2-d Dirac equation without any constants is represented usually as $$i*dt (\phi) = D (\phi)$$ where $D = m\sigma_2-i\sigma_1dx-i\sigma_3dy$. Where can I find explicit closed form solutions to ...
3
votes
1answer
442 views

Using Wien's Law to show spectral distruibution function of one temperature represents all temperatures

This is a exercise question from Quantum Mechanic textbook by Bransden: Using Wien's Law to show that if the spectral distribution function of black body radiation, $\rho(\lambda,T)$ is known at ...
6
votes
2answers
1k views

What is the definition of a quantum integrable model?

What is the definition of a quantum integrable model? To be specific: given a quantum Hamiltonian, what makes it integrable?
1
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1answer
374 views

How widespread is the meme “QM is counterintuitive” in academic physics? [closed]

I have recently entered university — studying CS — and I have spoken to many physics students on campus. Most of these — when propmted — will gladly proclaim that QM is ...
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2answers
412 views

Energy transfer using quantum entanglement

Can we transfer energy from one place to another separated by arbitrarily large distances without any time lag? For instance, if Alice and Bob are two observers making measurements having a singlet ...
5
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1answer
424 views

What fundamental reasons imply quantization?

In classical wave mechanics, quantization can occur simply from a finite potential well. In quantum mechanics, the quantization is obtained from the Schrödinger equation, which is, to my knowledge, a ...
0
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2answers
295 views

LS Coupling - weird image in the book

In the book by Arthur Beiser, Concepts of modern physics, in the chapter LS coupling there is this image: QUESTION: How do we get total orbital angular momentum $L=3$ (image (a)) out of quantum ...