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 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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59 views

probability amplitude and path integrals [closed]

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
73 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
62 views

What are observables? [closed]

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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56 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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59 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 ...
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4answers
208 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 ...
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1answer
86 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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27 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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32 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, ...
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1answer
34 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 ...
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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
87 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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41 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
53 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 ...
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96 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 ...
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1answer
68 views

Why according to Hund's first rule all electron with same spin should occupy orbitals when partially filling?

I get that because of coulomb repulsion initially all the electrons will not occupy the same site but will single occupy the orbitals.But while doing so how do they know to keep their spins aligned ...
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1answer
75 views

Eigenfunctions of Schrodinger equation

Why the solutions of the Schrodinger equation are called the eigenfunctions? For an electron moving in one dimensional lattice the eigenfunctions are given by$$\psi(x)=u_k(x)e^{ikx}.$$
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1answer
35 views

How are momentum and position operators dependent on the chosen inertial frame?

How are momentum and position operators in quantum mechanics dependent on the chosen inertial frame of reference?
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572 views

How to motivate Schrödinger's Equation? [duplicate]

Schrödinger's equation is supposed to be a differential equation for the wave function of a particle. As I currently understand, De Broglie's hypothesis is a hypothesis that for particles there should ...
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5answers
140 views

The meaning of Superposition

Is superposition purely conceptual or does it represent some real "thing"? Said another way, is superposition thought to have some tangible physical manifestation or is it simply the lack of physical ...
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1answer
143 views

How do creation operators change with time in an interacting theory?

When studying the quantization of a field theory with free fields, the creation operators $a^\dagger(k)$ are independent of time. In an interacting theory, they are time-dependant, and therefore ...
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2answers
140 views

What's the Cause of Quantum Entanglement? [duplicate]

What is the cause of quantum entanglement? When two particles become entangled what property of them basically changes as to establish a link between them and how the information is exchanged between ...
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648 views

Simple example showing why measurement & interaction are different

Does someone know of a clear (pedagogical) example where one can really see(with the math) where interaction and measurement are not synonymous in quantum mechanics? I know that every measurement ...
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137 views

Does the Hermitian operator $H=-\frac{d^2}{dx^2}$ have imaginary eigenvalues?

In quantum mechanics, Hermitian operators play a very important role because they possess real eigenvalues. Considering $-\frac{d^2}{dx^2}$, it is a Hermitian operator (Actually it's the simplest ...
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What is the physical process in paramagnetic resonance

In our QM lectures, Prof introduced an phenomenon called paramagnetic resonance, which described an electron precession in an $z$-direction magnetic field. I didn't quite understand this phenomenon, ...
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1answer
26 views

Allowed energies for semi-harmonic oscillator

Question: If a particle is attached to a semi-harmonic oscillator (that is, for example, the spring is stretchable but not compressible) such that the potential $V(x)$ is infinity for $x\leq0$ and ...
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3answers
148 views

Spectral properties in Solid state physics

So assume we have a periodic 1d Schrödinger operator $$- f'' + V(x) f(x)= \lambda f(x)$$ and we want $V$ to be periodic. Now if we assume that we are on a finite interval and that we have periodic ...
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338 views

Plants and Quantum Mechanics!

So, I have been working on quantum biology and found something interesting that I would like to write an equation for: Scientists have wondered how plants have such a high efficiency in ...
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1answer
51 views

Heisenberg Hamiltonian for spin-spin system

I wonder how we should conclude the following Hamiltonian (I mean the 32-18 in the picture below, written in solid state physics by Ashcroft & Mermin.) for spin-spin system? (It is in chapter 32 ...
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110 views

What's the connection between the spin of the photon and the polarisation of light?

In view of wave-particle duality, the spin of the photon must have a counterpart in the wave picture: is this polarisation?
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1answer
66 views

Double slit experiment query

Seen as thought empty space in a vacuum is not empty is it not possible that the gluon fields that remain affect the trajetory of an electron when carrying out the double slit experiment affecting the ...
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2answers
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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3answers
62 views

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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1answer
40 views

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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1answer
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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35 views

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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1answer
59 views

Are there any viable toy models of superdeterministic quantum mechanics?

As far as I know, superdeterminism in quantum mechanics is only considered as a theoretical possibility. Are there any fleshed out superdeterministic toy models so far which isn't nonlocal?
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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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127 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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1answer
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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66 views

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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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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43 views

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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3answers
32 views

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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5answers
190 views

How does a Wavefunction collapse?

I have been wondering and researching... How does a wavefunction collapse into one state?More specifically, what conditions cause a wavefunction for a quantum particle to collapse? Does this have to ...
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3answers
534 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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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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“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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98 views

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 ...