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 does fermi level in the band gap mean?

what does it mean that the fermi level for some smeconductores lie in the band gap? is fermi level definition different from what is know as usual? we define the fermi level as the highest level of ...
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2answers
15 views

How can the thrust due to radiation pressure be amplified in photonic laser thruster?

The thrust is amplified due to repeated bouncing of photons between two mirrors as shown in the diagram in this: Why does repeated bouncing of photons produce amplified thrust when the answer in ...
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3answers
40 views

Interpretation of Orbital Magnetic Moment

The wavefunctions for atomic orbitals have always been described to me one of two ways: As a "smeared out" electron standing wave with integer number circumference of de Broglie wavelengths As a ...
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1answer
47 views

A conceptual question about spin

I read in Landau's quantum mechanics that if the Hamitonian does not involve spin, the total wave function can be written $$ \psi ( x_1, x_2, ...) \chi ( \sigma_1 , \sigma_2 ,...)$$ in which ...
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1answer
509 views

Why is the light reflected at the same angle from mirror?

From the school physics I know that the material objects bounce from the plain surface at the same angle, losing some kinetic energy. In the same school I was taught that the light (and waves in ...
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1answer
42 views

How does a rotation operator change the angular momentum of a quantum system?

I think I'm having some problems understanding the role of rotation operator $$\mathscr {R} = e^{-i/\hbar \hat{L_z} \theta}.$$ Suppose we have a quantum system in the state $\vert \psi_0 \rangle$ ...
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3answers
245 views

Some small questions about quantum spin and rotations

I'm studying about quantum-spin (in a syllabus about non-relativistic quantum-mechanics though), but I have some trouble understanding everything. So I would like to ask some small questions, which ...
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3answers
39 views

General question about the potential barrier problem: Why does $\exp( kx)$ diverge when $x>0$ in the case when $E < V(x)$?

For the two images below, the first potential barrier has particles approaching it where $E > V_o$ & the second has a particle that has $E < V_o$, where $E$ is the energy of the particles ...
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3answers
162 views

Non-locality in non-relativistic Quantum Mechanic

I guess the following obvious question is answered by any flavor of relativistic Quantum Mechanics, but I just wanted to check whether I understand correctly: Is it correct that nonrelativistic QM ...
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5answers
326 views
+100

Difference between spin and polarization of a photon

I understand how one associates the spin of a quantum particle, e.g. of a photon, with intrinsic angular momentum. And in electromagnetism I have always understood the polarization of an EM wave as ...
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0answers
8 views

Charge density waves: site-centering v.s. bond-centering

Question about charge density wave (CDW): From this Ref. page 13, why bond-centering charge density wave is naturally compatible with the observed coexistence of charge ordering and ...
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1answer
30 views

Wigner's Theorem and discrete Symmetries

According to my skript: A pure state is a ray: $\quad$ $\{λψ\}$, where $ψ ∈ \mathcal H$, $||ψ|| =1$ fixed and $λ ∈ \mathbb C$, $|λ| = 1$. Pure states are uniquely given by 1-dimensional orthogonal ...
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0answers
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In the Penrose interpretation of QM, do electrons have a location in the atom before it is measure/observed?

I know that Bohm's interpretation says that it has a location before it is observed. Is that because it is a realist interpretation of QM? Do all realist interpretation of QM believe that electrons ...
2
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1answer
120 views

Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation ...
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1answer
86 views

In Quantum mechanics, what is realism? [on hold]

Some interpretations of QM are realist and some are anti-realist. But, it is the idea that something exists before it is measured, correct?
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1answer
40 views

Resource cost and noise effects in quantum teleportation of multible (entangled) qbits

Suppose you have n qubits that are in an unknown state (may be entangled, etc). Can you teleport this state by teleporting each qubit individually (using a Bell state and a classical channel)? If ...
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0answers
32 views

Electron doesn't have a location before it is measured?

Does this apply to all theories or just some? What about interpretations that are realist and don't require an observer, in those interpretations does an electron have a location?
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1answer
65 views

How do we normalize a delta function position space wave function? [duplicate]

I have a position space wavefunction $$\psi(x) = \delta(x-a) + \delta(x+a).$$ Now the question states to compute the following: The Fourier transform of $\psi(x)$. (Which invariably is the momentum ...
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1answer
35 views

Probabilities of pure states and density operators

According to my skript: A pure state is a ray: $\quad$ $\{λψ\}$, where $ψ ∈ \mathcal H$, $||ψ|| =1$ fixed and $λ ∈ \mathbb C$, $|λ| = 1$. Pure states are uniquely given by 1-dimensional orthogonal ...
1
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0answers
36 views

What information is contained in the quantum spectral density?

Consider a harmonic oscillator system with Hamiltonian $$\hat{H} = \frac{1}{2} a \hat{u}^2 + \frac{1}{2} b \hat{v}^2 \qquad [\hat{u}, \hat{v}]=i \gamma $$ where $a$, $b$, and $\gamma$ are all real. ...
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1answer
46 views

How can I write the anderson hamiltonian as a matrix? [on hold]

How can I write this Hamiltonian: $$ H = \sum E_d \hat{n}_d + \sum_k \epsilon_k\hat{n}_k + \sum_k V_{kd} (\hat{a}^\dagger_k \hat{a}_d + \hat{a}^\dagger_d \hat{a}_k) $$ in matrix form using its ...
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1answer
66 views

Do electrons have a location before they are observed/measured? [on hold]

Is this in all interpretations of QM? What about interpretations that are realist (MWI, penrose, ect)?
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1answer
84 views

Atom in a box and collapse of the wave-function

Suppose I have an atom trapped in an optically transparent box. I'm assuming the atom is bouncing off of the walls and not bonding, i.e. the center of mass of the atom experiences a square well. Now ...
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0answers
16 views

Spontaneous breaking order and the Peierls order

From this this Ref, several types of orderings are considered. Question: What are the Hamiltonians which support the Peierls order? Do they necessarily break translational symmetry or break the ...
3
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1answer
128 views

Poles for a particle scattered in a delta potential

I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also ...
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0answers
42 views

Hydrogen 2p3/2 -> 1s1/2 transition polarisation and angular distribution

Could you please help me. I have to calculate the intensity angular and polarisation distribution in hydrogen electric dipole transition $\text{2p}_{3/2}\rightarrow \text{1s}_{1/2}$. To do this I ...
2
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0answers
68 views

Quantum vs classical degrees of freedom

It is sometimes stated that any classical underpinnings (rightly non-local) of a general quantum system are unrealistic or unphysical because these require exponentially more information to store what ...
4
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1answer
315 views

What is crystal field anisotropy or effect ? It forces the magnetic moment to point in particular local direction..

Can you give a basic explanation of what is crystal field anisotropy ? What is the reason to arise ? In spin ice it forces the dipoles to point in the local 111 direction. For partially filled rare ...
4
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2answers
161 views

Shot noise at high frequencies (can it really be ideal white noise?)

Quantum shot noise (either optical intensity noise or electrical current noise) described by the noise spectral density of $2 e I$ (electrically) or $2 h \nu P$ (optically). So it is white noise. I ...
4
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2answers
138 views

How do we know that photon entanglement isn't the result of the photons's states being predetermined?

I know there is evidence that it is not predetermined and I tried reading articles on it but most of them either don't explain the intuition behind the experiment or they speak in a foreign language ...
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1answer
108 views

Noise spectrum of two systems and interacting Hamiltonian

I've been discovering recently the concept of noise spectrum, defined as: $$S_{xx}[\omega] = \int dt \langle x(t)x(0)\rangle \text{e}^{-i\omega t}$$ Roughly the Fourrier transform of the two-point ...
3
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2answers
206 views

Hydrogen atom: potential well and orbit radii

I happened to open up an old solid-state electronics book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level En" The orbit radius is ...
2
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2answers
49 views

Why don't we have particles whose wavefunctions are symmetric wrt one exchange operator and anti-symmetric wrt other exchange operator?

Consider a system with $n$ identical particles. Let the wavefunction of the system be $\psi(r_1,\ldots, r_2)$. Let $P_{a,b}$ represent the exchange operator which exchanges particle $a$ with particle ...
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0answers
13 views

Nuclear spin relaxation, quasi-particle energy and spin spectral density

Below is a measurement of the longitudinal nuclear spin relaxation ($1/T_1$). Ref: Fig 4 of page 24 Competing ground states in low dimensions. My question concerns the statement in this Ref that: ...
1
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1answer
29 views

Boundary Conditions in a Step Potential

I'm trying to solve problem 2.35 in Griffith's Introduction to Quantum Mechanics (2nd edition), but it left me rather confused, so I hope you can help me to understand this a little bit better. The ...
18
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1answer
617 views

Local explanation of the Aharonov-Bohm effect in terms of force fields

Here is an interesting paper for the Physics SE community: On the role of potentials in the Aharonov-Bohm effect. Lev Vaidman. Phys. Rev. A 86 no. 4, 040101 (R) (2012). arXiv:1110.6169 ...
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4answers
2k views

What really cause light/photons to appear slower in media?

I know that if we solve the Maxwell equation, we will end up with the phase velocity of light being related to the permeability and the permittivity of the material. But this is not what I'm ...
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0answers
29 views

Is FTL information transfer possible in an experiment involving entangled particles and an “available” black hole?

We consider the classical entanglement experiments involving Alice and Bob, and their entangled particles. It is proved that nothing that happens at Bob's end has any immediate effect on Alice's ...
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0answers
19 views

Expectation value calculation using Hermite polynomials [on hold]

I am facing this problem of not being able to correctly determine $x^2$ expectation value using the eigenfunction for harmonic oscillator involving Hermite polynomials as derived in the analytic ...
5
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5answers
186 views

How do we know that electron wave function extends to infinity?

Why do physicists assume this? Is it a proven fact that wave function extends to infinity or just a theory? Would it make sense if they didn't extend to infinity?
1
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1answer
123 views

Are wave functions real physical objects? [duplicate]

Are wave functions (ex. electron waves) real physical objects or just mathematical tools?. Some researchers say that they have proof that they are real objects. Here's [the link] ...
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0answers
15 views

Electron wave function question?

In interpretations of Quantum Mechanics that are Psi Ontic, in which the wave function is REAL ( Objective collapse theories, MWI, ect), does the wave function still physically spread to infinity? I ...
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1answer
41 views

What is the implication that the Schrodinger equation be solved by both real and imaginary part of the wave function? [on hold]

Suppose $\psi = \psi_{real} + i \psi_{imag}$ be the wave function, then both $\psi_{real}$ and $\psi_{imag}$ can be used to solve the Schrodinger's equation This can be demonstrated by plugging ...
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1answer
55 views

Configuration Space And Hilbert Space For A Physicist Without Knowledge Of Analysis

I have passed calculus course, have basic knowledge of complex numbers and passed introductory linear algebra course. I am trying to study Griffith Quantum Mechanics book, but I am also checking some ...
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0answers
9 views

Calculation of the Lowest Energy of the trial wavefunction [on hold]

After a calculation of the lowest energy using two variational parameters a and b it is found that: E(a,b) = (3a+b)^2 - ab What is the optimal (minimum) value of E If I expand the bracket and ...
2
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2answers
37 views

Slater's determinant for Bosons/Symmetric Particles?

For Slater's determinant it is obvious how this describes two or multiple fermions/anti-symmetric particles. By definition the determinant introduces a negative sign in front of the second product. ...
12
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1answer
83 views

Connections between classical mechanics and quantum mechanics [duplicate]

I've been studying quantum mechanics and classical mechanics for a little while now, and I still don't feel as though I fully understand the motivation for some of our choices in Heisenberg mechanics. ...
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1answer
48 views

Why $2j+1$ number of states?

In this statement from Modern Quantum Mechanics by J.J. Sakurai: If $j$ is an integer, all $m$ values are integers; if $j$ is a half-integer, all $m$ values are half-integers. The allowed ...
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1answer
65 views
+50

How to minimize the wavepacket dispersion?

This is a final exam problem. Here is what I can remember: We know that if an electron's wavefunction starts out as a narrow wavepacket, and moving in a region of constant potential, then the ...
6
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6answers
325 views

Why quantum states are classified using only conserved quantities?

While studying quantum mechanics from standard textbooks I always felt some conceptual gap that was never mentioned or explained. In what follow I tried to formulate my question, please be patient ...