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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Impervious nature of solid matter due to quantum degeneracy pressure

On Wikipedia the following statement is made without reference: Freeman Dyson showed that the imperviousness of solid matter is due to quantum degeneracy pressure rather than electrostatic ...
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Why does the creation operator take a continuum value for the momentum?

Imagine that you have a lattice and a set of masses. Each mass at a lattice point. Now each two neighbouring masses are connected with spring. Now in Classical Mechanics (CM) the ground state is the ...
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Does classical physics predict the effects of shining a laser at a hair?

The discussion on this webpage mentions that shining a laser beam at a hair produces an effect like that of the double-slit experiment. Does classical physics predict the effect you observe when you ...
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234 views

What is the difference between quantum cryptography and quantum teleportation?

Generate two entangled photons, send one to a message sender and the other to the intended receiver. Both the sender and the receiver recover the same piece of quantum information from the photons, ...
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389 views

Uncertainty principle in infinite potential well

Consider infinite potential well i.e. Hilbert space $L^2 \bigl([0,1]\bigr)$. Next we consider subset $$D_\theta = \left\{ \psi \in L^2 \bigl([0,1]\bigr) | \; \psi \; \text{is absolutely continuos and ...
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Interpretation of the Random Schrödinger Equation

I should preface this by admitting that my physics background is rather weak so I beg you to keep that in mind in your responses. I work in mathematics (specifically probability theory) and a paper ...
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How Light or Water Intensity is equal to square modulus of wave function of Light or Water Waves $I=|\psi|^2 \,$?

I've seen the Wave Function as a psi $\Psi$ $\psi$. And always heard that the wave function is the Complex Number as Imaginary and real number. But I've never seen it I've never seen components of ...
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193 views

Quantum communication

Is it possible to get two atoms to opposite quantum states of one another so when I change the state of first one, the state of the other one changes too? Is it possible to move them to another place ...
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Is the collapse of the wave function inherently time asymmetric?

Schroedinger's equation, as we all know, is time symmetric. In quantum field theory, we have to come up with a more sophisticated CPT reversal, but the essential point remains unchanged. However, the ...
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matter wave and wave function

Is there any mathematical relationship between matter wave (or de Broglie wave) and wave function? Also, does each type of particle (e.g. photon, electron, positron etc.) have its own unique wave ...
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Angular momentum operator and expectation values

I was reading some notes and it says that $\langle L_z^2\rangle=\langle L^2\rangle$ IFF the system is radially symmetric. I can see that in order that the LHS of the statement implies that $\langle ...
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Describing quantum intereference with only currents and densities

I know about and believe to understand the general wave equation based Kirchhoff diffraction formula, which in the Fraunhofer limit leads to a farfield complex wave function by Fourier transforming ...
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Given entanglement, why is it permissible to consider the quantum state of subsystems?

Quantum entanglement is the norm, is it not? All that exists in reality is the wave function of the whole universe, true? So how come we can blithely talk about the quantum state of subsystems if ...
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Did anyone claim that quantum theory meant lasers would never work

I've been reading 'How the Hippies saved Physics', which describes a design for a superluminal communication device, of which the crucial part was a laser which duplicated an incoming photon many ...
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391 views

Examples of exact many-body ground state wavefunction

Is there any non-trivial many-body system for which the exact solution to Schrödinger's equation is known? (By non-trivial, I mean a system with particle-particle interactions.) Perhaps something like ...
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Particles for all forces: how do they know where to go, and what to avoid?

Here's an intuitive problem which I can't get around, can someone please explain it? Consider a proton P and an electron E moving through the electromagnetic field (or other particles for other ...
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Eigenvalue of $L_z$

In section 4.3 of Griffths' "Introduction to Quantum Mechanics", just below Figure 4.6, the sentence begins Let $\hbar \ell$ be the eigenvalue of $L_z$ at this top rung... Why is this valid? ...
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Backward causality: A question/extension to Ma et al.'s “Experimental delayed-choice entanglement swapping”

In a philosophically rather interesting experiment, Ma et al. show that backward causality exists in quantum physics. An Ars Technnica-article gives a less technical account. From Ars Technica: ...
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Fermi statistics and Berry phase

When the positions of two fermions are exchanged adiabatically in three-dimensional space, we know that the wave function gains a factor of $-1$. Is this related to Berry's phase?
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225 views

How could $\textbf{S}^2$ not be a multiple of the identity?

I'm self-studying quantum mechanics with Sakurai's book (Modern Quantum Mechanics, 2nd edition) and came across the following in reference to the operator $\textbf{S}^2$: As will be shown in ...
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Creation and Annialation Operators and Kinetic Energy Matrix Elements

I'd like to write equations for $c_{ij}(t)$, With a hamiltonian of the form $$H=\sum_{kn}a^{\dagger}_k t_{kn}a_n + \frac{1}{2}\sum_{klmn}a^{\dagger}_k a^{\dagger}_l v_{klmn}a_m a_n$$ with $t_{kn}$ ...
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Simple step in time evolution of position operator in simple harmonic motion

When considering the 'Heisenberg' picture of the harmonic oscillator, I've come across the step: $$\begin{align} \left\langle n\left|(\hat{q_H}\hat{H}-\hat{H}\hat{q_H})\right|k\right\rangle &= ...
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Fractional statistics

A common way to show that anyons exhibit fractional statistics in 2D is by arguing that the paths of two anyons winding round each other cannot be continuously deformed to zero. This seems to assume ...
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Concept of a point particle in quantum mechanics

A point particle is usually thought of as structureless and without dimension. However, given that Heisenberg's uncertainty principle prohibits us from knowing the position of a particle exactly, what ...
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What can tunnel through a graphene sheet?

In popularizations, people tunnel through walls or doors. But what can really tunnel through a graphene sheet without tearing it? According to Wikipedia, a single layer of graphene absorbs 2.3 % ...
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Spectrum measurement

How can be spectrum of hydrogen measured (Lyman series, Balmer series, Paschen series and so on)? I mean schema of measurement circuit and the measuring technique (including all the steps needed). Is ...
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Probability of getting a particular spin

I'm a beginner in quantum mechanics, and I'm a bit confused about states and the probability to measure certain values. I would like to understand at least the following simplified situation: ...
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Classical limit of a quantum system

If we have a one dimensional system where the potential $$V~=~\begin{cases}\infty & |x|\geq d, \\ a\delta(x) &|x|<d, \end{cases}$$ where $a,d >0$ are positive constants, what then is ...
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What areas of physics should a mathematician study to understand TQFT?

I am studying topological quantum field theory from the view point of mathematics.(axiomatic treatise) So it has no explanation about physics. I would like to know physic background of TQFT. But I ...
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Hydrogen radial wave function infinity at r=0

When trying to solve the Schrödinger equation for hydrogen, one usually splits up the wave function into two parts: $\psi(r,\phi,\theta)= R(r)Y_{l,m}(\phi,\theta)$ I understand that the radial part ...
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How can we know about particle spin? [duplicate]

Possible Duplicate: How does one experimentally determine chirality, helicity and spin? This is a rough quite from Hawking: "An elementary particle with 0 spin looks the same no matter ...
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Can randomness exist?

Considering every cause has an action, how can anything be random? For something to happen, it must have a cause and through that definition it can't be random. Considering this why are many quantum ...
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Why can't two or more objects exist at the same place at the same time?

Two objects with half spin would consist of the elementary particles (i.e. quarks, fermions etc.) which are waves. Therefore all objects consist of several waves. Waves can exist at the same place at ...
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Angular Momentum Addition Theorem - Sanity Check

Looking back at my quantum mechanics notes, the angular momentum addition theorem is listed as: $j=j_1+j_2,j_1+j_2-1, ..., |j_1-j_2| $ (Using conventional notation) , but I'm a little unsure how to ...
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If randomness doesn't exist, how come the universe isn't a perfect sphere with predictable distribution of matter?

I'm presuming that the scientific community pretty much agrees that randomness doesn't exits, and that everything has a cause. Please correct me if I'm wrong, I've heard of quantum mechanics, but as ...
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Would Quantum entanglement theoretically allow prediction of the future?

This article describes how a choice made by the recipient of an entangled photon can affect measurements taken on that photon's "partner" before the decision was made. So let's say there are two ...
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Computing a density of states of Hamiltonian $ H=xp$

How could I compute the integral $$ N(E)~=~ \int dx \int dp~ H(E-xp) $$ the 'Area' inside the Phase space is taken for $ x \ge 0 $ and $ p\ge 0 $? The result should be $$ N(E)~=~ ...
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eigenvalue staircase and hamiltonians

Let two Hamiltonians $H_{1}$ and $H_{2}$ be defined in such a manner that their eigenvalue staircases satisfy $ N_{1} (E) = N_{2} (E)+A +O(E^{-1})$ What can we say about their potentials $ V_{1} ...
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687 views

Entanglement spectrum

What does it mean by the entanglement spectrum of a quantum system? A brief introduction and a few key references would be appreciated.
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Electric dipole transitions/expectation value of position

Part of a homework question asks to show that for $\ell=0$ in both $\Psi_i$ and $\Psi_f$, we have $$ \int \Psi_i^\ast \vec{r} \Psi_f \; d\tau = 0 $$ for the position vector $\vec{r}$. (This is for ...
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654 views

Operators Uncertainty

$\hat A$ is an operator. The uncertainty on $\hat{A}$, $\Delta A$ is defined by: $$\Delta A=\sqrt{\langle\hat A^2\rangle - \langle\hat A\rangle^2}$$ what is difference between $\langle\hat ...
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Validity of Einstein Coefficient Derivations

Consider a two-level energy gap with electronic energy states $E_1$ & $E_2$ and associated population densities $n_1$ and $n_2$ with $E_2>E_1$. In the derivation of the Einstein coefficients ...
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Again about all-win lottery

I suggest the following thought experiment that describes a machine which makes everybody happy. Suppose a lottery is conducted. The winner is awarded a billion dollars plus the title of eternal ...
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What is the support for the suggestion that reality is a computer simulation? [duplicate]

Possible Duplicate: Does Quantum Physics really suggests this universe as a computer simulation? I know the title sounds far-fetched, but the idea was first brought to my attention by a ...
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Is it necessary to use all solutions when calculating an expectation value in a spin state?

I'm given an spinor $\Psi$ which is solution of the Free Dirac equation, such that is an eigenfunction of $\hat{\vec{p}}$ and has positive energy. Then I'm asked to calculate the expectation value of ...
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403 views

Feynman's sum over histories?

The concept requires all possible path's to be mapped out, and any remaining paths not cancelled out represent the most probable path of the object. Considering this: i) If "infinite" paths are ...
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What is a Hilbert space filter?

In a recent paper, Side-Channel-Free Quantum Key Distribution, by Samuel L. Braunstein and Stefano Pirandola. Phys. Rev. Lett. 108, 130502 (2012). doi:10.1103/PhysRevLett.108.130502, ...
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Heisenberg Uncertainty Principle scientific proof

Heisenberg's uncertainty principle states that: if the x-component of the momentum of a particle is measured with an uncertainty $$\Delta \vec p_x$$ then its x-position cannot, at same time, be ...
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mechanism of annihilation

Can the annihilation of matter and antimatter be explained by the electro-weak interaction? Can pair-production be explained in the same way?
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Isn't the uncertainty principle just non-fundamental limitations in our current technology that could be removed in a more advanced civilization?

From what I understand, the uncertainty principle states that there is a fundamental natural limit to how accurately we can measure velocity and momentum at the same time. It's not a limit on ...