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 is relationship between Quantum tunnelling and Gravitational potential energy of stars?

Are there a direct mathematical relationship between Quantum tunnelling and Gravitational potential energy of stars? The true source of the Sun's energy was shown by Hans Bethe to be nuclear fusion ...
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3answers
66 views

Why would classical correlation in Bell's experiment be a linear function of angle?

Sorry if it's a newbie question, but I have trouble understanding the following part in the Wikipedia's explanation for the Bell's theorem: With the measurements oriented at intermediate angles ...
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9answers
13k views

Why don't electrons crash into the nuclei they “orbit”?

I'm having trouble understanding the simple "planetary" model of the atom that I'm being taught in my basic chemistry course. In particular, I can't see how a negatively charged electron can stay ...
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2answers
112 views

Two explanations of non-zero atomic radius

I have came across two separate explanations for why atoms have a positive atomic radius (as opposed to electrons "collapsing" into the nucleus). The first is via Heisenberg Uncertainty Principle, ...
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2answers
84 views

How do photons “decide”?

I was reading that when horizontally polarized light hits a vertical Polaroid all the light is blocked out. But when the Polaroid is off the vertical, some but not all photons "decide" to jump into ...
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2answers
32 views

Observing a particle over a certain domain

I was just thinking: in Quantum Mechanics, we start out with that whole collapsing business by observing the x position of a particle. I was thinking: why do we have to do that? What if we only ...
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35 views

Degeneracy in One Dimension

I'm reading this wikipedia article and I'm trying to understand the proof under "Degeneracy in One Dimension". Here's what it says: Considering a one-dimensional quantum system in a potential ...
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1answer
80 views

Quantum Excitations

In the context of quantum mechanics, is the Schrödinger equation actually describing some sort of an actual wave in some field like light in EM field ? So all particles are actually waves in their ...
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3answers
494 views

What is the Hilbert space of a single electron?

Is it the same as the space of all possible descriptions of a single electron? If not, how do they differ? Please give the mathematical name or specification of this space or these spaces.
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29 views

How to carry out the perturbation expansion of an anharmonic oscillator to high orders?

I think this is a standard problem in quantum mechanics. Consider the anharmonic oscillator $E \psi = \left(- \frac{1}{2} \frac{\partial^2}{\partial^2 x } + \frac{1}{2}x^2 + \epsilon x^4 \right) ...
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3answers
250 views

What does the Schrodinger Equation really mean?

I understand that the Schrodinger equation is actually a principle that cannot be proven. But can someone give a plausible foundation for it and give it some physical meaning/interpretation. I guess ...
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2answers
159 views

Measuring non-commuting observable at once

Given an Hilbert space $H$ (finite dimensional for sake of clarity), and two non-commuting operators $$A = \sum_a a |a\rangle\langle a|$$ and $$B=\sum_a b |b\rangle\langle b|,$$ is it possible to find ...
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27 views

Reduce density matrix for given eigenfunction [on hold]

My question is about how to find reduce density matrix for partition of given eigenfunction. Full question is just in image.
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2answers
186 views

The strange thing about the maximum in Planck's law

I read that it makes a difference whether you calculate $\frac{d \omega}{d \lambda}=0$ or $\frac{d \omega}{d \nu}=0$ in the sense that the maximum energy densit with respect to the wavelength does not ...
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0answers
35 views

Can be this configuration used to faster than light communication?

I know from some popular science articles or books that is possible to make special pairs of particles which are quantum entangled. Then each of entangled particles can be moved to different places ...
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2answers
125 views

Infinitely many degeneracy of Landau level: Countable or Uncountable?

Description of Landau levels can be found in many standard textbooks of quantum mechanics and here. Two ubiquitous solutions apply either the symmetric gauge $\vec{A}=(-\frac{1}{2}By,\frac{1}{2}Bx,0)$ ...
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5answers
192 views

Meaning of probability in a multiverse/a many-world interpretation?

Consider me tossing a coin and I got tail as a result on observing it. Then, what would be the result of the 'parallel me' in another universe? If the 'parallel me' gets head as a result then, ...
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3answers
124 views

Can two single particles interfere with each other?

Groups of particles can interfere with one another; In the double slit experiment when measuring single photons at the screen each one arrives at the screen in a random manner and they only show the ...
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1answer
44 views

Expectation value of number operator $\hat{n}$

I'm studying for my quantum mechanics test and I've stumbled on this problem. They want the expectation value of $\hat{n}$, $\langle \hat{n} \rangle$, with this given $\psi$ at $t=0$: $$ \lvert ...
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4answers
991 views

Does the observer or the camera collapse the wave function in the double slit experiment?

Ok so if we setup a camera before the slit we will find a single photon and will follow through accordingly, likewise by having a camera setup after the slit, we can retroactivly collapse the wave ...
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+100

What methods exist to calculate the density of states in the continuum of a molecule?

Say I have an arbitrary molecule in the Born-Oppenheimer approximation, and furthermore say that I can approximate the molecule as having only one active electron. What methods exist to calculate the ...
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2answers
176 views

On deriving Schrodinger Equation

I do know that one can't actually derive any axiom, but here is my serious attempt to explain Time Independent Schrodinger Equation with minimum preliminary knowledge. In the following $f$ is ...
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1answer
40 views

Forward-scattering off a potential well

In his book, James Binney writes the following: My question is what is the meaning of this expansion as $1+T$? I say this because you don't tend to consider the possible "paths" that a particle ...
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340 views

Reconstruction of “wavefunction” phases from $|\psi(x)|$ and $|\tilde \psi(p)|$

Consider a "wavefunction" $\psi(x)$, which has a Fourier transform $\tilde \psi(p)$ Suppose that we know, for each $x$, $|\psi(x)|^2$, and that we know, for each $p$, $|\tilde \psi(p)|^2$. Have we ...
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2answers
141 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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3answers
184 views

Entropy and the uncertainty principle

According to the second law of thermodynamics, the total entropy of the Universe must always increase after any interaction (as I understand). So in the hydrogen atom, the electron has a high ...
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1answer
210 views

Density matrix and irreducible tensor operators

I'm reading those lecture notes on atomic physics. Yesterday I posed a question on reducible tensors, and today I have a question on their relation to the density matrix. If there's any information ...
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Rabi oscillations with quantized light: which is the “quantum” effect, collapse, revival or both?

In wikipedia http://en.wikipedia.org/wiki/Jaynes%E2%80%93Cummings_model#History it is stated that It was later discovered that the revival of the atomic population inversion after its collapse is ...
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1answer
119 views

Why is the orbital angular momentum of a pi electron along the axis of two atoms' molecule one?

I'm reading quantum chemistry. The book says that the orbital angular momentum of a $\pi$ electron along the symmetry axis of a molecule made up of two atoms is $\pm 1$. I think this is a primary ...
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1answer
317 views

How can (in Dirac's terminology) the product of two “real” linear operators be “not real”?

I'm puzzled about a statement from Dirac's book, The principles of quantum mechanics, (§8, p.28): As a simple examples of this result, it should be noted that, if $\xi$ and $\eta$ are real, in ...
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65 views

Why is graphene the only (stable) 2D sheet structure? [duplicate]

I know that Carbon molecules can form different structures depending on how they bond with each other: graphite, diamond, graphene and fullerene. As far as I understand, graphene is just a "sheet" of ...
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1answer
59 views

Commutativity of Position Operators

Does the position operator $q_{i}$ of one harmonic oscillator commute with the position operator $q_{j}$ of another different harmonic oscillator? In other words, is $q_{i} q_{j} = q_{j} q_{i}$ true? ...
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1answer
76 views

Time evolution of a quantum system

A quantum system has Hamiltonian $H$ with normalised eigenstates $\psi_n$ and corresponding energies $E_n$ ($n = 1,2,3...$). A linear operator $Q$ is defined by its action on these states: $$ ...
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1answer
55 views

Scattering theory textbooks

I am looking for a possibly extensive list of great textbooks on elastic and inelastic scattering of particles within quantum field theory. So far I am familiar with: Peskin and Schroeder: An ...
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1answer
41 views

Why a hole in the Dirac sea can be seen as having opposite energy?

In the Dirac's old attempt of relativistic quantum mechanics, a hole in the $E'$ level of the Dirac sea was interpreted as a particle of opposite charge and positive energy. I do get why it can be ...
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0answers
20 views

Require Help for Graphene Based experiments [on hold]

I really need a software that can help me with graphene based experiments. Is there a software which could allow me to run all types of simulations for graphene layers focusing on photovoltaic cells? ...
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40 views

How to make scattering matrix? [on hold]

I need to make a scattering matrix. Potential is unknown. I have the list of scattering data: time, mass and coordinate of the particle. How to make scattering matrix by the given data?
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3answers
62 views

Can we apply Quantum Superposition

Erwin Schrödinger’s famous thought experiment's video presented by Perimeter Institute for Theoretical Physics. From this video can we conclude that , in a macroscopic label we can not have a ...
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32 views

Momentum of electron problem [duplicate]

Recently, my friend bemused me with a question related to the momentum of an electron. The confusing logic is stated below: Since an electron is a particle and according to classical physics, we know ...
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0answers
83 views

General wave packet in Schrödinger equation?

Can I state general wave packet in arbitrary potential $V(x)$ in the following form? $$\psi(x,t) = \frac{1}{\sqrt{2\pi \hbar}} \int \hat{\psi}(p,t) e^{ipx/\hbar}dp=\frac{1}{\sqrt{2\pi \hbar}}\int ...
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1answer
116 views

Is there a formalism for talking about diagonality/commutativity of operators with respect to an overcomplete basis?

Consider a density matrix of a free particle in non-relativistic quantum mechanics. Nice, quasi-classical particles will be well-approximated by a wavepacket or a mixture of wavepackets. The ...
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3answers
124 views

Can a bullet really fly through space forever?

Some people says that if it would be possible to shoot a bullet so high that it would get over the Earth gravitational pull, the bullet could fly through space forever, because of no deceleration of ...
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1answer
34 views

How to construct this oracle quantum gate?

I was reading the paper Quantum Computational Complexity in the Presence of Closed Timelike Curves. In this the author mentions that following quantum oracle gate which operates on $n+1$ qubits, can ...
2
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4answers
118 views

Bond Angles - H2O vs CO2

H2O has a 109.5 degree bond angle, but CO2 has exactly 180 degrees. Is there a qualitative reason for this? It's hard to believe CO2 is exactly 180 degrees unless there were some symmetry, but the ...
6
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1answer
74 views

Is there is a specific original source where the “quantum operator ordering issue” is stated?

During my research, when the quantum operator ordering ambiguity is mentioned is deemed usually in the likes of "the well-known problem of ordering in quantum mechanics". However, could anybody point ...
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18 views

How is it shown that the composition of two real operators is generally not real? [duplicate]

Dirac on page 28 of his QM book writes: Thus the conjugate complex of the product of two linear operators equals the product of the conjugate complexes of the factors in the reverse order. As ...
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1answer
51 views

Does a normal torch emit entangled photons?

I was reading a sciencenews.org post about three photons being entangled. My question here is, why is the chance of producing an entangled pair once in a billion times? Isn't every particle produced ...
3
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35 views

Entanglement g-2-experiment - Which components do I need?

I would like to measure whether my source emits entangled photon pairs. To that order I want to build a g-2-experiment, which measures photon coincidence counts as a function of time delay between ...
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3answers
202 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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1answer
45 views

How many wavefunctions are in a minimal basis set for benzene?

I am reading Modern Quantum Chemistry by Szabo and Ostlund and on page 62 he says "A minimal basis set for benzene consists of 72 spin orbitals." I tried to understand this number but failed. ...