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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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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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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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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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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216 views

Is the spin 1/2 rotation matrix taken to be counterclockwise?

The spin 1/2 rotation matrix around the $z$-axis I worked out to be $$ e^{i\theta S_z}=\begin{pmatrix} \exp\frac{i\theta}{2}&0\\ 0&\exp\frac{-i\theta}{2}\\ \end{pmatrix} $$ Is this taken to ...
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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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110 views

Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...
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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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211 views

Seeking a quality plain-language description of the Wigner-Eckart theorem

I'm a third year physics undergrad with a very cursory knowledge of quantum mechanics and the formalism involved. For instance, I understand roughly how tensors work and what it means for a tensor to ...
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181 views

Do Bell inequality violations appear instantly when the source is turned on, or do they increase over time?

This experimental Question is a result of reading a particular article on Bell violations. I addressed the e-mail below to the corresponding authors —because who knows, they might reply— but it is not ...
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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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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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157 views

Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...
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125 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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Hubbard Model Hamitonian

$H = -\sum\limits_{i,j} A_{ij} c_i^{\dagger} c_j + \frac{U}{2} \sum\limits_i(c_i^\dagger c_i)(c_i^\dagger c_i -1)$ is defined to be a Hamiltonian for modeling quantum random walk of identical ...
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121 views

Is there an idealist rather than realist interpretation of QM?

The many-worlds interpretation of QM is a realist explanation as it makes the wave function of the universe real. That is it makes the probabilities of outcomes real outcomes. One could argue that ...
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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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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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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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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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290 views

Coercivity of a ferromagnetic material?

I understand that coercivity is the field/force required to demagnetize/magnetize a ferromagnetic material. What if we had two opposite magnetic fields of different strengths values H acting on the ...
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239 views

Integers, Energy levels, and wavenumbers for a particle in a 2D box

(This question is not about coding) I have built a little code in Python that allows the user to plot the energy vs the wave number of particle in a 2D box, depending on what values for the integers ...
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77 views

A few questions on wave packets and uncertainty relations

According to Cohen-Tannoudji the wave-function for a one-dimensional free particle can be written as $$ \psi (x,0)=\frac{1}{\sqrt{2 \pi}} \int g(k) e^{ikx} dk.$$ While $g(k)$ is not specified, there ...
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Are these two quantum systems distinguishable?

Suppose Stanford Research Systems starts selling a two-level atom factory. Your grad student pushes a button, and bang, he gets a two level atom. Half the time the atom is produced in the ground ...
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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 ...
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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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“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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86 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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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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128 views

Quantum Mechanics in Electric Field

I am working on a problem which looks like this. Consider a charged particle with charge $q$ trapped in a box of length $L$ with finite constant potential $ V_0 $ on both ends. A constant (static) ...
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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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523 views

Classical analogue of Heisenberg and Schrödinger pictures?

What do the Heisenberg and Schrödinger pictures in quantum mechanics correspond to in classical mechanics (if they correspond to anything)? It's kind of weird, because (if I understand it well) in ...
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128 views

Stimulated emission direction

Place a sub-micron clump of crystal violet molecules in front of a multipixel detector. Raise the molecules to an electronically excited state with a beam of 590 nm light, illuminating from the side ...
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90 views

Difference: Fermi wave length vs. phase-breaking length?

I am reading a quantum transport book, where they often mention: phase breaking length and Fermi wavelength. I have looked up and found that: Phase breaking length= length over which electron remains ...
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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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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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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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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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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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68 views

Is something beyond the material needed to solve the Von Neumann Chain?

A problem has been presented that goes like this: Particles normally exist as several mathematical possibilities rather than one actual object. It is said that in the absence of observation, ...
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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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Consequences of the new theorem in QM?

It seems there is a new theorem that changes the rules of the game in the interpretational debate on QM: http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392 Does this only leave ...
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Perturbation theory with degeneracy even after 1st order

Most textbooks on basic quantum mechanics tell you that when your initial Hamiltonian $H_0$ has degenerate states, then before you can do (time independent) perturbation theory with a perturbation ...
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1answer
139 views

Is Ehrenfest theorem equivalent to Bohr's Correspondence Principle?

Ehrenfest theorem is usually dubbed as the quantum mechanical equivalent of Newton's law and Griffiths states, in the first chapter of his textbook, that Ehrenfests theorem enables us to work with ...
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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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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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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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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 ...