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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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 ...
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61 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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54 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
69 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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29 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
56 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
87 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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30 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
88 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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82 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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44 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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46 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 ...
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3answers
116 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 ...
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38 views

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
86 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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2answers
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 ...
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2answers
27 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
19 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 ...
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1answer
44 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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17 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
48 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 ...
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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. ...
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1answer
24 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
61 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 ...
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2answers
47 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
103 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?
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44 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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37 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
88 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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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 ...
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1answer
57 views

probability amplitude and path integrals [on hold]

Recently, I have been learning about path integrals and I was wondering, can the probability of a certain path be weighted more in a path integral? Said in another way, can certain paths have more ...
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3answers
72 views

Two-Particle System

I thought that the general composite wave function for Identical Bosons is: \begin{equation}\label{} \psi_{+}(r_1,r_2)=A[\psi_{a}(r_1)\psi_b(r_2)+\psi_b(r_1)\psi_a(r_2)] \end{equation} but I stumbled ...
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1answer
58 views

What are observables? [on hold]

What are observables and how are they related to quantum decoherence and wavefunction collapse. I read this: Observables - what are they? but it was about the technical details on observables. Even ...
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3answers
54 views

For the Uncertainty Principle, Do the Units of the Two Complementary Quantities have to Equal Js?

I know that the Uncertainty Principle is: $△P•△Q=ħ/2$. But do the units on the Left Hand Side of the equation always have to equal 'Js', i.e. Energy x Time (the same is the Plank Constant, $h$) or is ...
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2answers
57 views

Proof that quantum Fourier transform is unitary

I'm trying to work through the proof that the quantum Fourier transform can be described by a unitary operator, i.e $F^{\dagger}F=\mathbb{1}$, where ...
4
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4answers
188 views

What does observation mean in two-slit electron diffraction experiment? [duplicate]

My question is clear, that I ask: What do we mean by "observation" in 2-slit experiment for electrons (or any other wave-particle)? You know, we say that :"if we observe the electron, it shows a ...
5
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1answer
79 views

Equivalence classes in a Hilbert space

I'm reading something about quantum information/quantum computing theory, and I've run into a wall. I know what is meant by an equivalence class and how something can be partitioned into equivalence ...
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0answers
24 views

Double well potential [on hold]

A particle is in the following double-well potential with $E<0$: $$V(x)=0 \quad for \quad x<-a, x>a; -V_0 \quad for \quad -a<x<-b, b<x<a; 0 \quad for \quad -b<x<b$$ I am ...
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25 views

Why spin-$\frac{1}{2}$ nuclei have zero electric quadrupole moment?

Why spin-$\frac{1}{2}$ nuclei have zero electric quadrupole moment? How to calculate in general?
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24 views

Parity of magnetic susceptibility $\chi(\omega)$

It is well known that real and imaginary parts of magnetic susceptbility, defined as $\chi=\chi'(\omega)-\mathrm{i}\chi''(\omega)$, ought to be even and odd to frequency $\omega$ respectively, ...
2
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1answer
28 views

How does inflation relate to spontaneous matter creation?

According to Inflation for Beginners, ... quantum physics allows the entire Universe to appear, in this supercompact form, out of nothing at all, as a cosmic free lunch. The idea that the Universe ...
6
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2answers
166 views

Infinite dimensional vector spaces vs. the dual space

I just happened across this over on Math Overflow. It references the following theorem from linear algebra: A vector space has the same dimension as its dual if and only if it is finite ...
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1answer
85 views

Electron at rest

David Griffiths suggested a website in his book where I got this paper http://www.hep.princeton.edu/~mcdonald/examples/electronatrest.pdf Here the author says classically a particle at rest(in some ...
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2answers
40 views

How to connect Rabi frequency with absorption intensity?

If a particle with non-degenerate spectrum starts in some eigenstate, and the frequency of the external EM field matches some transition frequency, then this would lead the particle to do periodic ...
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1answer
51 views

using a given wavefunction to find particle properties

Let's say we have a given wavefunction and we want to find a particle that will fulfill the properties for that wavefunction. How can we do that? Is it possible? I was thinking of using Schrodinger's ...
0
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1answer
62 views

Bound States in quantum mechanics [on hold]

A particle is found in the following potential: $$V(x)=\infty \quad \text{for} \quad x<0;$$ $$V(x) = -V_0 \quad \text{for} \quad 0<x<a;$$ $$V(x) = 0 \quad \text{for} \quad x>a.$$ Given ...
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2answers
94 views

Need of vector potential in quantum mechanics

I need your opinions. Why is the vector potential of a magnetic field important (or even necessary) to quantum mechanics? Why it has to be defined everywhere? Is there any fundamental reason you can ...