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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“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
96 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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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
56 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
27 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
56 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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20 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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69 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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0answers
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 ...
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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 ...
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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
51 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 ...
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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 ...
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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
75 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
41 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
44 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 ...
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5answers
2k views

Quantum random numbers from a laser — simplest setup?

I'm a software / maths guy who would like to build a physical setup for generating quantum random numbers. I have no physics background, so bear with me. Background The project is for a public ...
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1answer
74 views

What's the deep reason for the velocity field of a wave function to be irrotational?

In quantum mechanics, the current of probability is $$\vec{v}=\frac{\hbar}{m}\mathrm{Im}\left(\frac{\nabla \psi}{\psi}\right)=\frac{\hbar}{m}\nabla S$$ where $\psi=R e^{i S}$ and $R$, $S$ are real ...
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2answers
112 views

About the postulates of quantum mechanics and self-adjointness

I am a freshman trying to understand the very basics of quantum mechanics but I met barriers at the beginning. What really matters is the postulates of quantum mechanics and their relationship with ...
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1answer
113 views

How does quantum decoherence occur?

My question is how does quantum decoherence happen. What happens with a quantum system when "observed?" Can you give a mathematical explanation that is simple, precise, and easy to understand?
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1answer
53 views

Naive interpretation of Galilean invariance of the TDSE

I was told today by someone smarter than myself that the time-dependent Schroedinger equation in one dimension was invariant under a Galilean transformation of $(x,t)$, namely under ...
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3answers
348 views

Why is Wheelers Delayed Choice Experiment Incorrect?

I have come across 'Wheelers Delayed Choice Experiment' which tries to prove that you can work out which Slit a Photon Goes Through in the Double Slit Experiment. But I thought it was impossible to ...
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1answer
56 views

Is operator $\hat{O}_{\alpha}:|\phi,\psi\rangle\mapsto |e^{i~\alpha[\phi,\psi]}~\phi,e^{-i~\alpha[\phi,\psi]}~\psi\rangle$ unitary?

Is the operator $\hat O_{\alpha}$ which is defined in the following a unitary operator? Operator $\hat O_{\alpha}$ is supposed to act on composite states with two explicit components, such that ...
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0answers
30 views

Rotational wave funtion of a nucleus

The rotational hamiltonian of an axially symmetric rotor is, in the intrinsic frame of the body, where the moment of inertia is diagonal, $$\mathcal{H} = \frac{\hslash^2}{2I} \left(J^2 - I_3^2\right) ...
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1answer
58 views

How does an operator transform under time reversal?

We know that a time-reversal operator $T$ can be represented as $$T=UK$$ where $U$ is some unitary operator and $K$ is the complex conjugation operator. Then under time-reversal operation, a quantum ...
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2answers
38 views

Can a two-levels photon pair be created either entangled or not entangled? [closed]

I am learning about experiments on Quantum Optics and Quantum Tomography in order to understand how to measure two qubits with an arbitrary quantum state of their polarization degrees of freedom. ...
1
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1answer
42 views

Proof of Kohn's theorem

In 1961 W. Kohn's paper ( Phys. Rev. 123, 1242 (1961) ) first stated that the electron-electron interaction does not change the cyclotron resonance frequency in a bulk three dimensional gas. I can ...
2
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1answer
124 views

Quantum Spin Simulation

In Leonard Susskind's Quantum Mechanics: The Theoretical Minimum, he describes a computer program that could fool you into thinking there is a quantum spin in a magnetic field. This spin is inside a ...
2
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2answers
66 views

is decoherence continuous?

Pardon my naivete here. In a quantum system, it seems that even a few photons from the environment can decohere the entangled particles in the system in a trillion trillionth of a second ( or faster). ...
3
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1answer
72 views

Quantum Wavefunctions Without Space

A handful of physicists have a rather peculiar definition of 'nothing' in terms of cosmology. Their claim is that the Universe, assuming it has 0 total energy, could have arisen from nothing but ...
2
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0answers
25 views

What property of medium is directly related to light propagation speed in that medium? [duplicate]

Refractive index is used to calculate phase velocity of light in medium, other than vacuum. Recently I had a discussion with somebody claiming that light is slower due to magnetic field of atoms. I ...
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1answer
30 views

Density matrix of a single qubit as a function of its Stokes Parameters

$\newcommand{\bra}[1]{\left\langle#1\right|} \newcommand{\ket}[1]{\left|#1\right\rangle} \newcommand{\prom}[1]{\langle{#1}\rangle} \newcommand{\matrixel}[3]{\bra{#1}{#2}\ket{#3}}$ How can I prove ...
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1answer
26 views

Electron interference and light interference

In the double slit experiment I see that shooting electrons one by one after long time create a pattern that resembles that of light interference, but before these long time I see electrons at ...
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2answers
100 views

Can you stop an electron in vacuum?

If we shoot an electron in vacuum tube, then stop it with electromagnetic field, and switch off the field, what will happen with electron? Will it continue its movement? If there is a gravitational ...