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 collapsed the wave function of organic molecules for life to form?

The wave function only collapses when it is measured by an observer. So, before life came into the universe, I'm guessing that everything existed in superposition. We are told life was formed as a ...
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22 views

Is nature quantized?

I was reading Planck's postulate the other day on Wikipedia and couldn't help but noticing the sentence: "...is the postulate that the energy of oscillators in a black body is quantized..." ...
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12 views

In MWI, how to make sense of the nonuniqueness of decomposing mixed states into pure states?

It's well known that in quantum mechanics, a generic mixed state can be decomposed into pure states in infinitely many different ways. While this property is kind of understandable if quantum states ...
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9 views

What is trivial and non-trivial gate in computing?

My question seems like it should be posted in Computer Engineering section, but below is how I found this word. I was reading the textbook: Quantum Computation And Quantum Information - by Michael A. ...
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35 views

Double slit experiment setup which resolves dualism

Suppose we have the following setup of double-slit experiment: A point source of coherent photons emits them so that they fall onto a non-transparent panel D ...
1
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1answer
36 views

Delayed Choice Quantum Eraser [duplicate]

All delayed choice quantum eraser experiments I've seen record the signal photons reaching detector D0 and then use the data of the idler photons recorded at detectors D1, D2, D3, D4 to "filter out" ...
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27 views

Best book for learning Quantum Communication [duplicate]

I am new in Quantum physics. I want to do my BSc thesis on Quantum Communication. My major is Communication. So I want to learn fast. I have little idea about quantum computing. So please suggest me ...
6
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3answers
705 views

Does quantum entanglement arise from quantum theory or is it merely an experimental observation?

I assume that entanglement emerges from quantum mechanics because the idea was around before experimental verification (e.g the EPR paper). How then does entanglement emerge from the theory (please ...
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1answer
38 views

Quantum Physics, Energy States [on hold]

Which of the following transitions in a hydrogen atom absorbs a photon of the highest energy? a.) $n=2\hspace{1cm}to\hspace{1cm}n=3$ b.) $n=3\hspace{1cm}to\hspace{1cm}n=2$ c.) ...
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26 views

How to minimize the wavepacket dispersion?

This is a final exam problem. Here is what I can remember: We know that if an electron's wavefunction starts out as a narrow wavepacket, and moving in a region of constant potential, then the ...
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3answers
121 views

About the double orthogonality of the eigenfunctions of the Hamiltonian

Consider the usual Hamiltonian describing the motion of a particle, $$\hat H = \frac {\hat P^2}{2m} + V(r),$$ where for simplicity the problem can be considered in 1D on the semiaxis $[a, \infty)$ , ...
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1answer
58 views

Can interacting Hamiltonians always be written in second quantized form?

Is it always possible to write interacting Hamiltonian in a second quantized matrix form like we do it for non-interacting form $$H=\sum _{\alpha\beta}C_\alpha^\dagger h_{\alpha\beta} C_\beta$$ ...
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2answers
59 views

Is light emitted in zitterbewegung? [duplicate]

Recently I heard of Zitterbewegung, a trembling motion of the electrons in atoms that arises from Dirac's equation. I know that, according to Bohr's model, light is emitted when the electron "jumps" ...
0
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1answer
26 views

Dipole approximation in solids

I have seen the use of dipole approximation (where the extent of the wave function is assumed to be much smaller than the wavelengths of the transitions or that of the electromagnetic field applied) ...
14
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2answers
2k views

Why don't we have a theory of everything?

What is currently stopping us from having a theory of everything? I.e. what mathematical barriers, or others, are stopping us from unifying GR and QM? I have read that string theory is a means to ...
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10 views

Minimum spread of frequency and wavelength in neodymium laser

What is the equation linking the minimum spread in wavelength and frequency of a pulsed laser, in relation to the lasers pulse time and operational wavelength. For example: If a Neodymium laser ...
0
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2answers
41 views

Linear polarization measurement - what QM observable is measured?

My understanding is that photon can have spin +-1 along propagation direction, corresponding to two circular polarizations. Linear polarization is superposition of two. Since one can measure linear ...
0
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1answer
100 views

Angular momentum needn't always change in multiples of $\hbar$?

I read the following claim in Slichter's popular book, Principles of Magnetic Resonance (after Fig. 4.3, it's p100 in this version.). Despite the title, the author claims it in a quite general manner ...
3
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1answer
110 views

About the nonlocality of QM and faster-than-light/backward-in-time machines

The fact the quantum mechanics is nonlocal is known already for a long time, since the Bell works (1966 and later) and the Aspect's group experiments confirming the Bell-type CHSH inequality (1980 ...
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1answer
59 views

Can Einstein's 'Theory of General Relativity' exist in Harmony with 'Quantum Mechanics'? [on hold]

From the Book 'In Search of Schrodinger's Cat': Coordinates in space-time represent position; causality depends on knowing precisely where things are going, essentially on knowing their momentum. ...
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2answers
80 views

What is the point of the reduced Planck's constant $\hbar$ (h-bar)? - Why don't we just have Planck's Constant $h$?

I know that $ħ$ is $h / 2π$ - and that $h$ is the Planck Constant ($6.62606957 × 10^{-34}$ $Js$). But why don't we just use $h$ - is it that $ħ$ is used in Angular Momentum Calculations?
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1answer
34 views

Are superoperators (CPTPM) equal if they are equal on all density operators?

$\DeclareMathOperator\tr{tr} $Is the following statement true? Conjecture: Let $\cal E_1,\cal E_2$ be completely positive trace-preserving maps (quantum superoperators). Assume that for any positive ...
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1answer
61 views

Amplitude $\langle0|e^{-iHT}|0\rangle$ in A. Zee's QFT In A Nutshell

In his Quantum Field Theory In a Nutshell, in page 12, (Second Ed), A Zee says that conventionally, the amplitude $\langle0|e^{-iHT}|0\rangle$ is denoted by $Z$. In the next paragraph, he considers ...
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2answers
90 views

can we detect the photons in the interaction of two charged bodies?

if the interaction of two charged bodies is through the photon exchange: 1) how much is the energy of these photons and how do we calculate their energies? 2) can these photons be detected by a photon ...
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32 views

Why Penrose's conjecture that consciousness is affected by quantum phenomenon too much of a stretch for Hawking [on hold]

Why did Stephen Hawking feels that Penrose's statement on quantum consciousness is too much of a stretch? This is a classical reductionist argument. Humans are made by atoms, atoms are made by ...
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1answer
101 views

Schroedinger Equation and Special Relativity

From what I understand, the Schroedinger equation describes how the wave function of a quantum system evolves in space over a given time (I am referring to a relativistic version of the Schroedinger ...
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88 views

Is there a textbook which covers QM via Geometric Algebra (GA)?

There is at least one good book on classical mechanics using Geometric Algebra (GA): New Foundations in Classical Mechanics by David Hestenes. Likewise there is at least one good book on classical ...
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52 views

Heisenberg picture with creation annihilation operators

In the Schrodinger picture, states are time dependent and operators time-independent. So expected values look like: $\langle s_1,t|\hat{A}|s_1,t\rangle$. If we go over to the Heisenberg picture the ...
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52 views

Quantum fluctuation

According to the quantum fluctuation concept, a particle and its corresponding antiparticle appear out of nothing only to annihilate and emit some energy in the form of electromagnetic waves. Does ...
1
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3answers
138 views

Non-locality in non-relativistic Quantum Mechanic

I guess the following obvious question is answered by any flavor of relativistic Quantum Mechanics, but I just wanted to check whether I understand correctly: Is it correct that nonrelativistic QM ...
4
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2answers
158 views
+50

How did the operators come about?

This relates a little bit to my previous question (Experimentally, what categorizes a measurement as corresponding to a certain observable?), but it's different in a way and more historical. One of ...
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7 views

High photon flux for ultrashort photons?

What is currently the highest photon flux one can achieve for single photons with a coherence length of femtoseconds? Does some know roughly know the order of magnitude? Unfortunately I was not very ...
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2answers
88 views

How do I calculate the most probable orbital an electron is in?

If I saw a snapshot in time of an electron near a proton (Hydrogen), then the electron can be in any orbital as long as it doesn't lie on a node of the wave function. So how would I determine which ...
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25 views

What probability distribution the detection counts have?

As far as I know in quantum mechanics each particle have a separate normalized wave function that can be used to calculate that the particle can be found somewhere. Or more practically to determine ...
0
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2answers
28 views

Constructing the singlet state by orthogonality

Every set of notes I can find says that the singlet state can be found by requiring that it be orthogonal to the triplet state with $S_z=0$ but they never explain how you actually do it. I can sort of ...
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1answer
20 views

Time Dependent Perturbation Theory Probabilities

(This is taken from Griffiths Quantum Mechanics): So suppose I have two states $\psi_{a}$ and $\psi_{b}$, and the particle starts out in the state $\psi_{a}$: $$ c_{a}(0)=1\qquad c_{b}(0)=0. $$ To ...
2
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1answer
47 views

Pauli exclusion principle for the protons in water

The Pauli exclusion principle applies to all fermions, right? And protons are fermions. So if you consider a water molecule, and swap the protons in the two hydrogens, shouldn't the wavefunction of ...
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18 views

AC Stark effect first order change in energy

I am looking at this paper http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=89946 where Eq (12) $\triangle E_{ii}(\tau)=-\frac{e\hbar}{m_{i}c}\bf{k}.\bf{A}(\tau)$ (where i=c,v) is mentioned as the ...
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1answer
50 views

Lorentz Invariance of the Dirac equation

My question is more conceptual than mathematical. As a differential equation the Dirac equation is invariant under Lorentz transformations. Conceptually though Lorentz transformations describe a ...
0
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1answer
39 views

Probability of superimposed states vs probability of separate states

Suppose there is an infinite square well where $\psi_1$ and $\psi_2$ are the ground state ($n=1$) and the first excited state ($n=2$), and each satisfies the time-independent Schrodinger equation. ...
0
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1answer
26 views

Spin Hilbert space

I'm currently doing some quantum mechanics and was able to transform my Hamilton operator to something that basically looks like this: $$ H = H_{xy} + \frac{p_z}{2M} + \alpha S_z, $$ where $H_{xy}$ ...
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2answers
64 views

problem with learning Quantum Mechanics [on hold]

I've started learning quantum Mechanics from " Griffiths " book and finished chapter one , but the problem is i feel most of what i'm doing is mathematics , for example he solved the problem of ...
0
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2answers
53 views

Experimentally, what categorizes a measurement as corresponding to a certain observable?

I want to write a computer program. The input to the program is: A description of an experimental device (for instance a Stern-Gerlach apparatus, or a laser and a polarizer) What the experimenter ...
5
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3answers
106 views

How do we know that the Fourier transform of space is momentum?

How do we know that the Fourier transform of real space $x$ is the momentum $p$ space or for energy and time, receptively? What's the mathematical process and physical logic?
0
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45 views

Do twice more atoms absorb twice more photons?

Let's assume you have a photon detector that detect individual photons striking it when exposed to a weak light source. Now let's assume you somehow managed to make a denser detector from the same ...
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60 views

A conceptual question about scattering theory in quantum mechanics

When defining the cross section, we use this formula $$ \psi_S = \frac{f(\theta,\phi)}{r} e^{ikr},$$ to prove this one $$ j_{out} = \frac{|f(\theta,\phi)|^2}{r^2} \frac{\hbar k}{\mu},$$ and then ...
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14 views

How to derive the electron dipole selection rule in coupled bases?

We need to find $| \psi_f \rangle$ fulfilling the condition that $$ | \langle \psi_f | \mathbf{x} | \psi_i \rangle |^2 \neq 0.$$ When using the uncoupled bases $| l,m,m_s \rangle$ I can derive the ...
3
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38 views

Cubic perturbation to coupled quantum harmonic oscillators

I recently came across this two-dimensional problem of a particle in a potential of the form $$V = \displaystyle{\frac{1}{2}m \omega^2} \big(y^2 + x^2y \big) - \alpha y,$$ where $x$ and $y$ are known ...
3
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1answer
89 views

Half integer eigenvalues of orbital angular momentum

Why do we exclude half integer values of the orbital angular momentum? It's clear for me that an angular momentum operator can only have integer values or half-integer values. However, it's not clear ...
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28 views

How does Dirac define the representative of $\{\langle\phi\frac{d}{dq}\}\psi\rangle = \langle\phi\{\frac{d}{dq}\psi\rangle\}$

On pate 89 of Dirac's book, The Principles of Quantum Mechanics, he writes: Let us treat the linear operator $\frac{d}{dq}$ according to the general theory of linear operators of section 7. We ...