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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Superposition principle

If $S=(v_{1},v_{2}......v_{n})$ is a basis for vector Space V, then every vector v in V can be expressed in the form of $v=c_{1}v_{1}+.......c_{n}v_{n}$ in an unique way. Explain the significance of ...
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1answer
55 views

Existence and Quantum Mechanics [closed]

I am not a physics major but I'm interested in studying quantum mechanics. Does matter (or energy, they're the same anyways :P) really gets created and destroyed very fast in a subatomic field or in ...
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71 views

What does it mean to expand a Hamiltonian using perturbation theory?

On UC Davis chemwiki website, the Hamiltonian for quadrupolar coupling in NMR is analyzed. (The details of this aren't important.) It is said in the analysis that: The expansion of the ...
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1answer
62 views

Justification of discrete spectrum for V(x) unbounded at $\pm \infty$ in Pauling and Wilson

In Pauling and Wilson, Introduction to Quantum Mechanics, they offer the following intuitive reason for the discrete spectrum of a potential which is unbounded at $\pm \infty$: This is ...
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100 views

I am learning Quantum Mechanics and I have some questions about some basic concept [closed]

What does a "STATE" exactly mean in quantum mechanics? What is the equivalence of "STATE" in classical mechanics? If we have a wave function $\Psi$ , its absolute square $|\Psi|^2$ is the ...
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98 views

Does electromagnetic field collapse the wave function of charged particles?

In an electron double slit experiment, let's put two charged plates behind the slits in an attempt to move the pattern up and down on the the screen. What will happen? Will it just shift the ...
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1answer
183 views

Explanation of Dirac's proof of arbitrary ket being expressible with eigenkets of observable

In P.A.M. Dirac's The Principles of Quantum Mechanics, Chapter 10 (Observables), pp. 40, at the end of the chapter there is a proof that I don't understand at all. Here is a pdf link to the book ...
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6answers
835 views

How can molecule of a few angstroms absorb visible light of a few hundred nanometers?

I guess visible light is visible, because it has the right wavelength to be absorbed (or not) and emitted (or not) by many different molecules. Now visible light has a wavelength in the order of a few ...
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47 views

Solution of the time independent Schrödinger wave equation using Green function [closed]

Green function are famous for solving inhomogeneous differential equations. However in some examples it is also used for solving the homogeneous differential equations. So is there any way that we can ...
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38 views

Noncanonical commutation relation and noncanonical wave mechanics

Consider noncanonical operators $\hat{x}_1,\hat{x}_2,\hat{p}_1,\hat{p}_2$ satisying the following condition in the $q_1,q_2$ - basis ($\psi=\langle q_1,q_2|\Psi\rangle$)(similar to wave mechanics): ...
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1answer
79 views

How is the theory of partial coherent light related to quantum-mechanics?

Background Let me start this question by a long introduction, because I assume that only few readers will be familiar with the theory of partial coherent light and concepts like a mutual coherence ...
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26 views

Radius dependence of Energy levels of spherical Quantum dots

I have frequently read in articles that the energy level of spherical quantum dots depends on radius. We simply match the wave functions inside and outside the particle and find the intersection of ...
2
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1answer
66 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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28 views

Does small objects still move “smoothly” or are there a measurable incrementation?

First off all: I'm no physicist so I am sorry if this question is badly written or stupid even. But it's so exiting to read and try to learn about this kind of stuff! Lets say you have a quark (or a ...
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1answer
39 views

What is the difference between Rayleigh scattering and Thomson scattering?

After reading the wiki articles I know, that both Rayleigh scattering and Thomson scattering are elastic processes. But what is the essential difference between those two processes, their cross ...
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1answer
28 views

In quantum entanglement are the 2 sub atomic particles exhibiting all possible values before being measured

I have been reading a lot about quantum entanglement when I came up to a part which says that before measuring one of the particles there is a 50:50 chance that a particle will be one of the pair but ...
5
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1answer
70 views

Is there still mystery about spin crisis?

The gluon is a vector boson; like the photon, it has a spin of 1. If this is true and if we know the spin of protons and neutrons then why the news SPIN COMES FROM GLUONS? is telling that, we ...
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1answer
74 views

Decoherence in Everett quantum mechanics

Take an initial state and its environment, $E$, as follows, $$ |\psi\rangle_i = |0\rangle |E\rangle + \sqrt{2}|1\rangle |E\rangle. $$ Suppose that I've written it already in the basis in which the ...
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3answers
121 views

How does quantization solve UV catastrophe in black body radiation? What would happen if there was no Planck constant $h$?

Planck's Law is $$I(\nu,T)=\frac{8\pi\nu^3}{c^2}\cdot\frac{1}{e^{h\nu/kT}−1}$$ This solves the UV catastrophe. For higher frequencies, intensity goes to zero. It does so because of $e^\nu$ not ...
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56 views

What happens to “large objects” within very small time periods?

What can we say about the state of "large things" within very small time periods? While reasonable (or "useful") divisions between classical and quantum physics are usually made in terms of size, ...
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1answer
144 views

Classical vs. quantum energy of the hydrogen atom

If I have an electron and a proton and calculate the classical energy which I get by bringing the electron from infinity to the distance of a Bohr radius to the proton, I get 27.2 eV, but the electron ...
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1answer
66 views

Is there a physical interpretation to invariant random matrix ensembles?

Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ...
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340 views

How can blackbody radition be explained by quantization?

I don't understand why quantization makes a peak on the blackbody radiation curve (so there is no UV catastrophe) and the relationship between that peak and quantization concept. When the blackbody ...
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2answers
109 views

A rigorous treatment of distributions in quantum mechanics

In many introductory courses to quantum mechanics, we see $\delta$-functions all over the place. For example when expressing an arbitrary wave function $\psi(x)$ in the basis of eigenfunctions of the ...
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Do particles behave like electromagnetic waves?

From double-slit experiments we know particles have wave-like behavior: they statistically form an interference pattern. My question is: Is this wave-like behavior similar to the photons' behavior? ...
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68 views

Does first quantization perturbation theory imply a large scale web of electron entanglement?

My question may seem quite esoteric given the title, but I think it's relatively straightforward when explained properly. Imagine a relatively simple situation of 2 hydrogen atoms (numbered 1 and 2), ...
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Suggest me specific book for studying scattering theory and special functions [duplicate]

I am doing msc physics. And we are studying major part of scattering theory. I used Quantum Mechanics by Davydov, Griffiths, etc, to study scattering theory. But I am not understanding it properly, ...
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59 views

Darboux theorem and the canonical decomposition of a two-fermion wave function

It is a classical theorem in quantum mechanics or quantum chemistry or quantum information that a two-fermion wave function has a beautiful canonical expansion: $$f(x_1, x_2) = \sum_{j=1}^N ...
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88 views

What does this question about entanglement and classical geometry mean?

Below is the question from Andy Strominger's presentation at the String 2014 conference. The question was asked by credible physicist Ashoke Sen as an important question. "What is the precise ...
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39 views

Bound states and continua in the spectral function

Okay, let me try hard to pose this question as clear as I can. Let's take a quantum system where a single charge carrier interacts with a bosonic mode. Examples would be the Holstein model where a ...
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63 views

Double slit experiment from first principles of QM

I have read many descriptions of electron double slit experiment but I could not find the description from the first principles of quantum mechanics. Most of the descriptions makes comparison with ...
1
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1answer
47 views

Sold-State Band Structure - connection between Fermi Energy, Fermi Level and Work Fuction

I've been struggling with the concepts of these three terms - Fermi Energy, Fermi Level and work fuction. Now, I was given these definitions (in the context of semi-conductors): Fermi Level is the ...
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156 views

Is entropy in quantum mechanics emergent or fundamental?

Since a quantum mechanical system, even an isolated system containing one particle, can be described by a density matrix, with entropy for the system given by $\langle S\rangle=-k \rho\ln(\rho)$, is ...
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1answer
47 views

Problem regarding quantum mechanical notation of photons

I have recently been reading about spontaneous parametric down conversion(SPDC). I do clearly understand the process. What has been intriguing lately is the notation. For those of you who are ...
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1answer
64 views

Is frequency or Bayesian interpretation used in quantum mechanics?

In quantum mechanics, we discussed about probability. There are two kinds of interpretations: frequency and Bayesian. Which one is actually used in quantum mechanics? My impression is, it doesn't ...
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1answer
55 views

Ultrafast photon detectors

Are there already photon detectors that can resolve the shape of photons in the time domaine if it looks like below where the two humps are separated by a time of the order of femtoseconds? What I ...
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3answers
78 views

Analytical problems with Green's function

I have a question about the right definition of the Green's function in physics. Why do we introduce (or not) an infinitesimal, positive number $\eta$ to the following definition: $$\left[ ...
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Double Slit Experiment with Two Independent Sources

Imagine a variation on the double slit experiment. I'll describe it in 2D using the $x-y$ plane. The $x$-axis is impenetrable other than the two slits, which are positioned at $(-1,0)$ and $(+1,0)$. ...
2
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3answers
43 views

Demonstration that vibrating basic particles constitute non-vibrating individuals

I am a dilettante in physics; I ask for pardon for my confusion-causing (if any) terminology usage, and also for my imprecise choice of question tags. I know that basic particles of any individual ...
2
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1answer
50 views

English translation of Heisenberg's paper ``Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik''

Is there any english translation of Heisenberg's paper Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik online? I have found not. Thanks so much.
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1answer
77 views

Supersymmetry definition

Can someone outline the difference between supersymmetry and supersymmetric quantum mechanics? I often hear the two used interchangeably but I'm almost certain they are not the same.
3
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3answers
127 views

In what limit do we *really* get Maxwell-Boltzmann statistics from Bose-Einstein and Fermi-Dirac?

Fermi-Dirac and Bose-Einstein energy occupation number $n(\epsilon)$ in natural units ($[T]=[\epsilon]$) read $$n(\epsilon) = \frac{D(\epsilon)}{e^{(\epsilon-\mu)/T}\pm 1},$$ where $D(\epsilon)$ is ...
2
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1answer
45 views

Paraxial wave equation solution?

I am looking for a worked solution to the paraxial wave equation, since most sources just say that clearly Gaussians are solutions but they do not explicitly show so. This equation is equivalent to ...
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2answers
143 views

Basic question on the Aharonov-Bohm effect

I have a very basic question on the Aharonov-Bohm effect. Why is the curve integral $\oint_\Gamma {A}\cdot d{r}$ non-zero ? $\Gamma$ is the "difference" of both paths $P_1$ and $P_2$. If the ...
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0answers
26 views

Two-photon absorption and 3rd order susceptibility

I am referring to introduction of Section 12.5 Multiphoton Absorption and Multiphoton Ionization (Page no. 550 of Nonlinear Optics, Boyd-3rd edition) where it has been said that the two-photon ...
3
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1answer
36 views

Quantum mechanics with non-cartesian coordinates

Let say we have the classical hamiltonian of a harmonic oscillator: $$H=\frac{p_x^2+p_y^2+p_z^2}{2m}+\frac{k_1x^2+k_2y^2+k_3z^2}{2}$$ and we want to find the hamiltonian operator in quantum mechanics, ...
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Why is effective mass of holes positive?

i am trying to understand this. I know that the effective mass of electrons or holes is calculated as: $$m^* = \frac{h^2}{(4\pi^2)\frac{d^2E}{dk^2}}$$ Now,if i look at this plot for example: I ...
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2answers
164 views

Mechanistic approach to quantum mechanics

It seems we attribute effects to particles, but why does it seem that we don't try to answer the question: how does it have this effect? For example, in modelling the hydrogen atom with quantum ...
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1answer
69 views

Schrödinger evolution for a Klein-Gordon equation

I have a problem with the transition from quantum relativistic wave equations (specifically Klein-Gordon equation) to QFT, since a lot of assumptions seem implicit. For example I have a problem with ...
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3answers
91 views

First quantization version of quantum field theory

In quantum mechanics, we have the word second quantization for identical particles. However, when dealing with localized states, first quantization version of quantum mechanics is also very ...