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's the connection between the spin of the photon and the polarisation of light?

In view of wave-particle duality, the spin of the photon must have a counterpart in the wave picture: is this polarisation?
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1answer
65 views

Double slit experiment query

Seen as thought empty space in a vacuum is not empty is it not possible that the gluon fields that remain affect the trajetory of an electron when carrying out the double slit experiment affecting the ...
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2answers
40 views

How are the components of the spin vector defined?

How do we distinguish between the $x$, $y$ and $z$ spin components? More precisely: how do we define the $z$ component? (according to what, it is the $z$?) for measuring the $x$ component how ...
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3answers
61 views

Schrödinger: Coherent states

A coherent state is called $\Psi_{{\alpha}} \left( x,t=0 \right)$ and is defined by: $a_{{{\it \_}}}\Psi_{{\alpha}} \left( x \right) =\alpha\,\Psi_{{\alpha}} \left( x \right) $ where $a_{{{\it ...
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1answer
36 views

Quantum mechanics: compatible observables

I am confused about something. If (all what I will write are operators) $x$ is compatible with $p_y$ that means they have the same eigenvectors. However, $x$ is compatible with $y$ which means they ...
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1answer
85 views

What are density matrices and how do they work?

I have looked in Stack Exchange about density matrices but haven't found any answers. What are density matrices and how do they work? What are they used for? (Also, please tell me what is wrong with ...
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0answers
35 views

Berry curvature and linear response functions

Let $\hat{A}^i (i = 1, . . . , n)$ be a set of hermitian observables and $F_i$ a corresponding set of external fields that are linearly coupled to $\hat{A}^i$. Starting from the ground-state at $F_i = ...
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1answer
59 views

Are there any viable toy models of superdeterministic quantum mechanics?

As far as I know, superdeterminism in quantum mechanics is only considered as a theoretical possibility. Are there any fleshed out superdeterministic toy models so far which isn't nonlocal?
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46 views

Wave-Particle Duality in the Confinement of an Electron in a Box [closed]

According to the wave particle duality, one can say that an electron is both a wave and a particle. If we confine it in a box, it can only form standing waves at particular wavelengths, which leads ...
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1answer
126 views

Has the Copenhagen Interpretation remained accurate?

Almost a century past, has the Copenhagen Interpretation (CI) undergone any modification? In other words, has any of its underlying principles been reformulated since? The notable (usual) examples ...
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1answer
84 views

Complex comjugate of Schrodinger equation: paradox in matrix form?

We can take the complex conjugate of schrodinger equation, and obtain $$ -\frac{\hbar^2 }{2m}\frac{\partial^2\psi}{\partial x^2} + V(x)\psi = i \hbar \frac{\partial \psi}{\partial t} $$ $$ ...
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1answer
66 views

How can I prove this inequality for a harmonic oscillator?

I need a hand with this problem. I have to prove that for a particle in any quantum state in an harmonic potential $$ \langle X\rangle \leq2\Delta E\Delta P/(m \omega^2 \hslash) $$ Here's my ...
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32 views

Does Zero Point energy imply acceleration?

Since there cannot be zero momentum in QM systems do such things as Zitterbewegung imply accelerations?
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2answers
43 views

A Quantum Telephone [duplicate]

You are an astronaut, traveling through space, but you ran out of fuel and need to get a hold of Houston immediately. How do you do it? You previously gave Houston one of two quantum particles that ...
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3answers
30 views

Commutation Relationship

For the Hamiltonian of the hydrogen atom, does the square of angular momentum, $$L^2 = L_x^2+L_y^2+L_z^2$$ commute with Hamiltonian operator, $$H = \frac{1}{2m}(p_x^2+p_y^2+p_z^2) + V(r)~?$$ Should ...
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5answers
187 views

How does a Wavefunction collapse?

I have been wondering and researching... How does a wavefunction collapse into one state?More specifically, what conditions cause a wavefunction for a quantum particle to collapse? Does this have to ...
3
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3answers
533 views

Why do we use the Coulomb potential for the hydrogen atom?

When solving the Schrodinger equation for the hydrogen atom, the Coulomb potential $V = \frac{e^2}{4 \pi \epsilon_0 r}$ is used. The Coulomb potential comes from classical electrodynamics, so why ...
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2answers
87 views

Why is quantum mechancis is not content with symmetric operators, but wants self-adjoint operators?

A symmetric operator has only real eigenvalues and different eigenvectors corresponding to different eigenvalues are orthogonal. These are exactly what we want for a physical observable. I think ...
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2answers
96 views

“Entangled photons never show interference in the total pattern without coincidence count” implies FTL

In my previous question, the most defended objection to the gedankenexperiment was that "Entangled photons never show interference in the total pattern without coincidence count". Here I show another ...
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3answers
98 views

Simple real-life examples of Fermi's golden rule?

I want to teach my students some simple applications of Fermi's Golden Rule. Unfortunately, most examples I can think of are in scattering theory, which they have not learned yet. Are there any ...
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0answers
14 views

What is the principle behind the use of one LASER for optical pumping of Rubidium in presence of magnetic field?

How can we use a single LASER for optical pumping of rubidium in the presence of magnetic field as the zeeman levels are degenerate in the presence of magnetic field and how to decide upon the ...
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5answers
2k views

How does the concept of a “black body” make any sense?

In my introductory chemistry class, we are learning about the basics of quantum mechanics. We were introduced to the concept of emission and absorption spectra. Our textbook describes how electrons ...
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1answer
49 views

Unitary transformation of the Hamiltonian with spin-orbital coupling

I am reading this Paper recently. The author says that: for this Hamiltonian: $$H(t) = \frac{p^2}{2m} + \frac{m\omega^2}{2}x^2 + \alpha p_x \sigma_y$$ If we make a unitary transformation ...
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1answer
58 views

Discrete vs Continuous spectra of operators [duplicate]

Why is it that if an operator $Q$ has a discrete spectra, that the eigenfunctions are all in Hilbert space? Why is it that if the spectrum is continuous we automatically know that the eigenfunctions ...
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2answers
54 views

From Quantum Mechanics to Statistical Mechanics in a Specific Case

I'd like to know how to get to statistical mechanics from the many-particle Schrodinger equation using a specific example, without using any Hamiltonian mechanics, phase spaces or ensembles, as a ...
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2answers
74 views

Does QM needs refinement?

Suppose atoms of an ideal gas are represented by non overlapping wave function so that the system can be described classically. As time passes the packets spread. Therefore over a period of time we ...
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1answer
28 views

What's the chance that each photon of an entagled photon pair passes through two polarizers?

This is a pretty basic question I think. But it's quite hard to find actual experimental results on the web (or maybe I don't know the right keywords). I'm new to quantum mechanics and want to ...
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1answer
57 views

How to entangle two particles? [duplicate]

After learning about quantum entanglement I wanted to know, what is the simplest way to entangle two particles in a lab?
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22 views

Quantum Chaos - Level spacing distribution in integrable quantum systems

For an undergraduate essay, I am studying the development of quantum chaos in a 1D spin 1/2 chain (my main source paper can be found here: ...
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2answers
54 views

How are electrons restricted to individual orbitals?

Since orbitals are just regions of electron density, they allow electrons to occupy the same space. I feel like in some sense this contradicts the Pauli exclusion principle limiting two fermions, or ...
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1answer
40 views

Double slit experiment: interaction with the environment

In order to recover the well-known interference pattern in the double slit experiment with massive electrons, one has to perform it in a vacuo. This is because, as far as I know, the interaction with ...
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2answers
70 views

How far back can you trace a photon?

You have a photomultiplier tube pointed at a distant star, exactly 100 light years away. It's perfectly set up so that nothing can get into the tube unless it came from that star. Every hour or so, ...
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1answer
35 views

Normalize Triplet State of Hydrogen

For hydrogen, the total spin of the electron and proton is $s = 1$, while $m_s = -1,0,1$. If $m_s = 1$, one of the states can be written as $$\left| 1\;1 \right > = \left |\uparrow \uparrow\right ...
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18 views

piezoelectric in quartz

Does any one know if it is possible to find the relation between the ac current frequency applied to a piezoelectric and the change in the crystal lattice due to this current BY USE OF HAMILTONIAN (in ...
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1answer
24 views

Introducing cut-off in a renormalisation procedure for quantum mechanics

I've been reading a paper on renormalisation theory as applied to a simple one-particle Coulombic system with a short-range potential. In the process of renormalisation, the authors introduce an ...
3
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4answers
221 views

What is the right order of creation operators?

I started to learn some basics of second quantisation and specifically its use in quantum chemistry. Currently I'm reading this book by Péter R. Surján, and here is small excerpt from it. If one ...
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2answers
257 views

Hilbert space and Hamiltonians

Assume a system described by a Hamiltonian H, and assume that the eigenstates of H, $φ_i$(r) are integrable in absolute square. We say that these states belong to a Hilbert space (they can even form a ...
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2answers
84 views

Why are atoms empty so much?

To clarify: My question is not Why are atoms empty?, my question is Why are they empty so much? The classical orbit of an atom, roundly speaking, is where the probability to find an electron is ...
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0answers
37 views

Path integral formulation for an optimization quantum mechanics problem

I have been working on a quantum mechanics problem I asked here and someone recommended to use path integrals. I learned about path integrals but I couldn't find out how to finding the most optimized ...
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0answers
17 views

What is Optimal Control Theory and Controllability Theory?

I was exploring the methods to analyze the evolution of a system from one quantum state to another using a suitable Hamiltonian. Some searching led me to the keywords Controllability Theory and ...
2
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1answer
23 views

Unitarity of a transformation, and reversibility, imply one another?

Are these concepts equivalent? And if not, which one implies the other one? A transformation Û is unitary when Û^{-1} = Û†. A reversible transformation  admits an inverse, Â^{-1}, that's all. ...
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0answers
55 views

Why does the time-independent perturbation theory become no longer useful when its order gets larger?

In Griffith's Introduction to Quantum Mechanics p. 256, after figuring out $$E_n^2=\sum_{m\neq n} \frac{|\langle\psi_m^0|H'|\psi_n^0\rangle|^2}{E_n^0-E_m^0}$$ he says We could go on to calculate ...
0
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1answer
41 views

Hamiltonian acting on sum operator

I am following a derivation in a book. It is implementing a state $|{\psi}\rangle$ into the eigenvalue equation $\hat{H}|{\psi}\rangle=E|{\psi}\rangle$. The $|{\psi}\rangle$ term contains a ...
0
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1answer
34 views

Spin operators commutation

Why do the spin operators $ S_{x1}$ and $S_{x2}$ of two particles along the $x$-axis commute i.e $S_{1x}S_{x2}-S_{2x}S_{1x}=0 $ ?
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1answer
38 views

Physical observables and hermiticity

Is it necessary for an operator to be Hermitian in order to be a physical observable or is it just sufficient that the operator obeys the eigenvalue equation? If I were to check whether an operator is ...
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0answers
20 views

Differential cross section for photon scattering on fixed magnetic dipole

Photon with energy $\hbar\omega$ scattering on a fixed particle with magnetic momentum $\vec{\mu} = \mu \vec s$. How to calculate a differential and total cross section for the photon. I've found in ...
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0answers
21 views

Independent boson model with an arbitrary finite-dimensional impurity

The independent boson model consists of the following Hamiltonian: $$ H_s = E \sigma^z $$ $$ H_b = \sum_k \omega_k b^{\dagger}_kb_k $$ $$H_{sb} = \sigma^z \sum_k (g_k b_k + g_k^{\ast}b^{\dagger}_k).$$ ...
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2answers
76 views

How is decoherence due to the environment compatible with the Copenhagen interpretation?

Let's say that "decoherence" is that transition from a pure quantum state to a mixed state due to interactions with the environment. (A reasonable definition?) How is that compatible with the ...
3
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1answer
42 views

Semiconductors and energy bands

The valence and conduction band of a semi-conductor are often drawn as here click. This plot has essentially two features and I would like to understand them. The peak and the valley of the two ...
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1answer
45 views

What is the density operator for an isothermal–isobaric ensemble (T,p,N)?

In the microcanonical ensemble $(E,V,N)$, the density operator is $$\hat{\rho}=\frac{\delta(\hat{H}-E\,\hat{I})}{Tr(\delta(\hat{H}-E\,\hat{I}))}$$ Where $\hat{H}$ is the Hamiltonian of the system and ...