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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Dirac representation between matter and anti-matter

If $|\psi \rangle$ represents a wavefunction through a column matrix and $\langle \psi |$ represents the dual vector in a row matrix and $|\psi \rangle \langle \psi | = \rho $ is the probability ...
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131 views

Change of operator in the Hamiltonian [closed]

We are told that the particle has mass m and charge e and is moving in 2 dimensions. The position operator $\mathbf{X}=(X_{1},X_{2})$ and momentum operator $\mathbf{P}=(P_{1},P_{2})$ We are given ...
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199 views

Virial theorem and variational method: an exercise (re-edited)

I have a hydrogen atom, knowing that its Hamiltonian has been modified turning the standard potential $$ V_{0}(r) = -\frac{Z}{r} $$ into $$ V(r) = -\frac{g}{r^{\frac{3}{2}}} $$ with $g$ a positive ...
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1answer
118 views

Harmonic oscillator

Let $|0\rangle,...$ be the states of the harmonic oscillator. Then a squeezed state was defined as $|\xi\rangle =S(\xi)|0\rangle $, where $S(\xi):=e^{\frac{1}{2}( \xi (a^{ \dagger ^2}-a^2))}$, where ...
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180 views

Shouldn't Quantum Mechanics change in a black hole?

I recently learnt that the conservation laws are a consequence of the symmetries of space and time (the Lagrangian in Newton mechanics). Since space-time change in a black hole wouldn't quantum ...
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1answer
93 views

Does this commutation relation hold?

I was wondering whether it is true that $[L_x^2,x^2+y^2+z^2]=0$. I could not find it in the internet and therefore I wanted to ask here whether anybody here knows that this is true or false.
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185 views

Non-locality and quanta

Quantum mechanics is non-local in that long distance correlations are present, though there is no signalling possible. But QFT is Lorentz invariant and contains quantum mechanics as a special case. I ...
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87 views

Born rule and Feynman propagators

Let us assume that we want to describe the full process of photon emission by electron A and absorption by electron B. Therefore electron B must be on the forward lightcone of electron A. In the ...
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1answer
210 views

Infinite potential square well solutions

My question is about understanding the different solutions of the potential square well. Imagine a square well defined this way: $$ V(x) = \begin{cases} ∞&\,{\rm if} x<0 \\ 0&\,{\rm ...
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3answers
166 views

Physically implementing quantum measurement of energy

If there were a particle in a box, how could one measure its energy? I understand the theory behind quantum measurements: the Hamiltonian operator represents the energy observable, so you perform an ...
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101 views

Ionizing an atom with a proton

What happens when a proton collide with an atom? How does the ionization occurs, assuming the proton has enough kinetic energy? How much energy is required for the proton to enter the atomic nucleus, ...
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229 views

Electron in a covalent bond: what happens when it moves out?

Let's look at a covalent bond in, say, a water molecule: H : O : H H is bonded to O by a pair of electrons. But electrons are in constant motion. What happens when the electron leaves? Why does ...
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5answers
326 views

The quantum state just after a position measurement

The wave function of a free particle is given as, $$\psi(x) ~=~ e^{-{ x }^{ 2 }/{ a }^{ 2 }}.$$ Then a position measurement is made and the position of the particle is found to be at $x=a$. My ...
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1answer
99 views

Interaction between neutrino and an anti-neutrino?

What happens when a neutrino and an anti-neutrino interacts together? For example, what does a muon neutrino and anti-muon neutrino produce? it says in my book that it creates "muons and antimuons". ...
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2answers
169 views

Which of these two different forms of spin-orbit interaction is correct?

I am seeing the spin-orbit interaction in two different ways: $\lambda [\mathbf{p} \times \nabla V]\cdot \sigma$ $\lambda [\nabla V \times \mathbf{p}]\cdot \sigma$ I don't see how these two ...
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108 views

What happens at the exact moment an electron absorbs a photon

For example let's have the hydrogen atom in its ground state and the electron gets excited by a photon. If we consider relativity the wave function cannot change instantly, right? The process has to ...
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179 views

What are the practical applications of quantum foundations?

Many quantum foundation researchers keep emphasizing that For All Practical Purposes (FAPP), quantum foundations are irrelevant. They even invented an acronym for it! Does that mean that quantum ...
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3answers
228 views

How can the reduction postulate be removed with the other postulates of QM still leading to correct predictions?

In the axiomatic presentation of QM, I've seen it stated many times that the reduction postulate is not needed and/or incorrect, and could be gotten rid of. However, without the reduction postulate, ...
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714 views

DIY Quantum Eraser Experiment by the Scientific American: Is this really quantum?

Click here for the publication. Having performed this experiment, I have gotten clean results. Essentially, a double slit is made by putting an photon beam in the way of a wire with orthogonal ...
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1answer
708 views

How do I show that the eigenstates of a Hamiltonian can be made orthonormal?

I've been tearing my hair out over this all evening. It should be simple but I must be missing something somewhere. Can someone show me how to prove that the eigenstates of a Hamiltonian can be made ...
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1answer
88 views

Geometric Interpretation of Rotated basis of Hamiltonian and collective Dicke states

Suppose I start with a basis of states for a two spin-1/2 particle system, namely, $\{\left|\uparrow\uparrow\right\rangle, \left|\downarrow\downarrow\right\rangle, ...
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2answers
384 views

Do eigenvectors of quantum operators span the whole Hilbert Space?

I am trying to solve an exercise in Shankar's QM book (concretely 4.2.1), and I am asked the probability of each possible value for the operator $L_x$ when the particle is in a certain eigenstate of ...
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1answer
1k views

Is it that electron of an atom can be found anywhere in the space?

Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found. The diagrams cannot, ...
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3answers
188 views

Quantum Physics Books [duplicate]

I`m very newbie in physics and want to study on amateur level. I`m interested in Quantum Physics, can anybody advice some books?
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2answers
108 views

Diagonalization of this Hamiltonian: How do I transform the differential operators?

In order to find the eigenstates of this Hamilatonian $$ H = \sum_{j=1}^3 \left( - \frac{\hbar^2}{2m} \frac{\partial^2}{\partial x_j^2}\right) + \frac{1}{2} m \omega^2 \left( (x_1 - x_2)^2 + (x_1 - ...
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1answer
89 views

Does measurement prevent tunneling?

Does observation collapse the wave function, thus preventing an object from tunneling to a classically forbidden region? If I understand correctly, observation causes objects to collapse into the ...
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563 views

Does the wave function always asymptotically approach zero?

I'm new to quantum physics (and to this site), so please bear with me. I know that quantum mechanics allows particles to appear in regions that are classically forbidden; for example, an electron ...
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295 views

Spin eigenvalues and eigenvectors problem. Is this the correct way to solve it?

An electron is described by the Hamiltonian $ H=\frac{e}{mc}\bar{S}\cdot\bar{B} $ where $\bar{S} =(S_x,S_y,S_z)$ is the spin operator and $\bar{B}$ the magnetic field. For $t>0$ ...
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53 views

How does the Planck length hold true? [duplicate]

If there is a length which no object can breach in terms of the smallest of size, how can that length hold true? Our earth is undoubtedly considered the Planck length to some monolithic planet out ...
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2answers
172 views

Without apparatus can we say that the system is measured(decohered) by the environment?

"Einselection" and "tridecompositional uniqueness theorem" seem to resolve the preferred basis problem. But the premise is that there are three parts in discussion.(system, apparatus, environment) ...
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1answer
829 views

Can a macroscopic body have wavelength as that of electron? [duplicate]

Einstein has suggested that light can behave as a wave as well as like a particle i.e, it has dual character. In 1924, de-Broglie suggested that just as light exhibits wave and particle properties, ...
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118 views

How can the pre-measurement be fulfilled?

In the decoherence program, the pre-measurement refers to the evolution in which the system and apparatus form a Schmidt state. In Maximilian Schlosshauer's review article(2005), I read "the linearity ...
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317 views

Evaluating commutator of $[\operatorname{sign}(X),\, \operatorname{sign}(P)]$

I wish to evaluate the following commutator: $[\operatorname{sign}(X),\, \operatorname{sign}(P)]$. Is there a general method for evaluating $[\operatorname{f}(X), \operatorname{f}(P)]$? I thought of a ...
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2answers
166 views

Calculating states of entangled and disentangled qubits

I'm writing a quantum computer simulator (about 8 qubits) and I know most of the basics (i.e. how to calculate the effect of a quantum gate on a qubit). But I have hit a wall. Is it possible, with ...
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3answers
102 views

At what point is the spin determined in a Stern-Gerlach Apparatus

Consider a particle with spin that travels through a Stern Gerlach box (SGB), which projects the particle’s spin onto one of the eigenstates in the $z$-direction. The SGB defines separate trajectories ...
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187 views

Inexact measurement and wavefunction collapse

As is usually said, measurement of an observable $q$ leads to collapse of wavefunction to an eigenstate of the corresponding operator $\hat q$. That is, now the wavefunction in $q$ representation is ...
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3answers
212 views

Why does a wavefunction collapse when observation takes place?

Why does a wavefunction collapse when observation takes place? Can this question be explained in non mathematical terms? I have tried finding the answer but couldn't find a clear explanation.
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49 views

General relativity && quantum mechanics “incompatibillity” [duplicate]

Now this may be utterly weird layman-physics-question, but anyways... I have read recently following: "The fundamental universe laws are everywhere the same. It's just that the manifestation (!) of ...
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3answers
328 views

What exactly is a bound state and why does it have negative energy?

Our professor hasn't explained what bound states are. Could you give me an idea of what they mean and their importance in quantum-mechanics problems with potential (e.g. a potential described by a ...
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2answers
966 views

Wave function with a delta potential

I have a particle and a potential $V(x)=\frac{\hbar^2}{2m}k\delta(x)$. Where $\delta (x)$ is the Delta function, and I am interested in the solutions of the stationary Schroedinger equation. If ...
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1answer
240 views

Energy and time evolution of a particle in a potential well

Hoping this is not a silly and stupid question let me ask for help in this problem. I have a particle in an infinite square well (the box is from 0 to a), in the state described by the function ...
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1answer
2k views

Photons and phonons

A few months ago I asked about phonons. I got some very good answers but I still have difficulty getting an intuition for phonons, while somehow photons, which in many ways are similar and which I ...
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155 views

Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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31 views

Edge states at high magnetic field (Quantum ballistic transport)

I am learning about edge states at high magnetic field (Quantum ballistic sample). What I understand so far from it is that at high magnetic field, Landau states arise. Then (I don't know exactly ...
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2answers
160 views

Does the photon emitted by an electron falling to a lower energy level have a direction?

When an electron falls from an energy state to a lower one, electromagnetic radiation is emitted. Is this equally emitted in all directions (as a spherical wave) and can we only give it a direction ...
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2answers
373 views

Does light have mass/weight?

If I plug in my memory stick/USB into my laptop and load it up with documents etc. will its mass/weight increase?
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1answer
112 views

Is the resistance 0 in the ballistic regime?

Given that in the ballistic regime a particle (electron) can move freely without scattering (there are no impurities ), is the resistance through a ballistic sample zero?
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1answer
88 views

Development/history of Mesoscopic Physics/quantum transport

I am studying mesoscopic physics/quantum transport. Now I am wondering (out of interest): how did this field emerge and what made it such a huge field? I couldn't find this somewhere clear on the web ...
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45 views

What are the ways of finding the spin of a particle [duplicate]

How many ways are there for this mission? Any article about that on the internet. I heard about TODAI made a reprogrammable quantum computer. Any more ideas are welcome
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1answer
93 views

Is it possible to make an optical lense that is an analog to a gravitational lense?

There are many lenses that do all sorts of things. eg. horshoe lenses twist light, meta material lenses can boggle the mind. Is it possible to make an optical lense that is an analog to a ...