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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Quantum Yang-Mills Theory and AdS/CFT

I just read the first chapter of Becker-Becker-Schwarz. To quote: A remarkable discovery made in the late 1990s is the exact equivalence (or duality) of conformally invariant quantum field ...
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1answer
39 views

Rate of change of a normalised wave function

I'm reading Weinberg's Lectures on QM. On top of p23 it says $$i\hbar\frac{d}{dt}\int|\psi(x,t)|^2d^3x=i\hbar\int\psi^*(x,t)\frac{\partial}{\partial ...
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36 views

Bound states in 1D & 2D

Why does Mother Nature allow bound states in arbitrarily weak attractive potential in 2D but not in 3D? See, for example, this article: ...
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2answers
121 views

Dimension of separable state

I'm from a pure mathematics background (BSc and MSc). I’m reading Quantum Computing: From Linear Algebra to Physical Realization by Nakahara. Please can you help me to understand how the dimension ...
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3answers
45 views

What does “coherent wave function of a macroscopic body” mean?

What is meant by the "coherent wave function of a macroscopic body"? I found this phrase in a paper on QM, but am unfamiliar with the terminology.
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2answers
132 views

Inner products with orthonormal bases

Probably a stupid question here - I think it's a case of me not having sufficient mathematical background to follow this through. In Leonard Susskind's Theoretical Minimum book, he represents the ...
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3answers
49 views

Can we make a camera that fits in one of the bands of the double slit experiment?

So, in Young's double slit experiment, we see where the particle lands on the back wall. What if we were standing at the back wall, looking toward the slits? Could we gain more information not by ...
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0answers
61 views

Lack of scale in Schrödinger equation for square-inverse potential

I see that if we set our potential in schrodinger equation to be a inverse-square dependence we don't have a typical unit of length as we have for hydrogen atom. $$-{\hbar^2\over 2m}\nabla^2\psi + ...
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1answer
61 views

Quantum field theory: field operators in terms of creation/annihilation operators

I am learning Quantum Field Theory and there is a step in my notes that I do not really understand. It starts with the classical definitions of position $q$ and momentum $p$: $$ q = ...
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2answers
72 views

$\exp(i\alpha\hat {\bf n}\cdot{\bf \sigma} )=\cos\alpha I+i(\hat {\bf n}\cdot{\bf \sigma})\sin\alpha$

Could anyone tell me $\hat {\bf n}\cdot{\bf \sigma}$ is defined in such way? In the book they have not defined what is $n_z,n_x,n_y$. It is from Quantum Computing: From Linear Algebra to Physical ...
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31 views

Notation in a paper on quantum mechanics and gravitation (2)

I am currently reading the paper "Gravitation and quantum mechanics for macroscopic objects" by F. Karolyhazy (1966). The author defines formally rigorous equations in order to describe the decay of ...
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1answer
99 views

What does the notation $\Psi_k/(\Psi_k,\Psi_k)^{1/2} $ mean?

I am currently reading the paper "Gravitation and quantum mechanics for macroscopic objects" by F. Karolyhazy (1966). In his paper, he uses certain notation that I haven't come across before (he also ...
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3answers
379 views

Can someone please qualitatively explain unitary group from a physics perspective?

Unitary Groups is the most mysterious thing for me when studying physics. All my physics endeavor ends when author starts talking about unitary groups. This is often the case because in a lot of the ...
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3answers
42 views

Quantum Scales and the Flatness of Space-time

I know that on the smallest scales, general relativity predicts that space-time is flat. But I've also read that space-time can be described as a sort of "quantum foam" for distances smaller than the ...
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0answers
52 views

Why there is limit to size of the atom? [on hold]

As far as I know quantum mechanics does neither put an upper limit to the outermost orbit of an atom nor a lower limit to the radius of the ground state. Even quantisation of angular momentum never ...
4
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1answer
107 views

Why do people look for a field formalism for String Theory

String theory was originally formulated from a perturbative description (using quantum mechanics (QM) and replacing points by strings and evaluating path integral). Still, although QM has an upgrade ...
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1answer
68 views

Was the firewall paradox resolved?

For quite sometime there has been a claim that the firewall paradox has been resolved (via lasers). For instance, http://global.ofweek.com/news/Lasers-to-solve-the-black-hole-information-paradox-9867 ...
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66 views

General definition of vector spinor and spin

I am looking for basic and exact definitions of fundamental physical consepts in graduate level. I reach this following definitions. Could you please help to improve these definitions. Spin: ...
3
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1answer
104 views

Glauber's Formula

In the Cohen-Tannoudji Quantum Physics book, Complement BII, says: [...] two operators $A$ and $B$ with both commute with their commutator. An argument modeled on the preceding one shows that, if we ...
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1answer
90 views

What measurement of time is so small that it qualifies as quantum?

Quantum mechanics (QM; also known as quantum physics, or quantum theory) is a branch of physics which deals with physical phenomena at nanoscopic scales where the action is on the order of the ...
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61 views

Integral over a product of two Green's functions

Need some help here on a frequently encountered integral in Green's function formalism. Forgive me since I am a junior student. I have an integral/summation as a product of a retarded and advanced ...
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0answers
34 views

Quantum chaos in interacting discrete time quantum walk?

I have situation where I am simulating discrete time quantum walk (DTQW) for various graphs. I have two quantum walkers on the graph and they can interact with each other by the fact that where the ...
4
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2answers
87 views

“Delayed choice” quantum imaging experiment - why wouldn't it work?

I was just reading a Nature news article (Entangled photons make a picture from a paradox, 27 August 2014) about a way to form an image of an object out of photons that have not interacted with the ...
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1answer
57 views

Continuous spectra of photons

I guess this is a basic quantum mechanics problem, but I'm not entirely sure of my answer. Suppose we have an electron in a hydrogen atom having the state \begin{equation} ...
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5answers
323 views

Commutator algebra in exponents

Considering $X$ and $Y$ such that $[X,Y]=\lambda$, which is complex, and $\mu$ is another complex number, prove: $$e^{\mu(X+Y)}=e^{\mu X} e^{\mu Y} e^{-\mu^2\lambda/2}$$ My attempt (so far) is: ...
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0answers
44 views

What forces determine the distance of the electron from the proton in a hydrogen atom? [closed]

I mean to conceptually grasp the size and shape of the hydrogen atom's 1s orbital. I've seen it explained in terms of electrostatic energy and the Pauli Exclusion Principle. If possible, please ...
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1answer
49 views

Gaining symmetry through boundary conditions

Can Hamiltonian gain/lost some symmetry through boundary conditions? Initial expression may not have symmetry, but after specyfing boundary conditions and predicted form of the wavefunction it will ...
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0answers
25 views

Bell State Measurement From Parametric Down Conversion Source

My question is about whether or not there exists any scheme to distinguish between symmetric and antisymmetric Bell states from entangled pair of down converted photons. State of Down Converted ...
2
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1answer
52 views

Measurement of observables with continuous spectrum: State of the system afterwards

Suppose my system, described by a separable Hilbert space $H$, is in the state $\Psi$ when I measure an observable that has only continuous spectrum. What is the state of the system after the ...
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0answers
37 views

Correlation between Relativity and Quantum Mechanics [closed]

By which theory we can connect Quantum Mechanics and Relativity?
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0answers
26 views

Momentum operator of a particle in an electromagnetic field

In quantum mechanics, to all observables correspond some self-adjoint operators. In the absence of an electromagnetic field the momentum operator is clearly $\vec{P}:=\frac{\hbar}{i}\vec{\nabla}$. ...
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1answer
46 views

Is quantum indeterministic? [duplicate]

The question might look clear from a viewpoint of a non-physics guy but let me be more specific. Can we say quantum leaps or waves or maybe the universe itself are completely indeterministic or do ...
4
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1answer
57 views

Is the harmonic oscillator potential unique in having equally spaced discrete energy levels?

I was wondering if the good old quadratic potential was the only potential with equally spaced eigenvalues. Obviously you can construct others, such as a potential that is infinite in some places and ...
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1answer
68 views

What is the status of Everett's Thought Equation?

Here is Hugh Everett's PhD Thesis: http://philosophyfaculty.ucsd.edu/faculty/wuthrich/PhilPhys/EverettHugh1957PhDThesis_BarrettComments.pdf On page 9 he says: "We have the task of making ...
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0answers
73 views

The relationship between angular and linear momentum

Why is orbital angular momentum not 0 when spin and linear momentum are not collinear? Why can it be 0 when spin and linear momentum are parallel? Like in the example of a scalar field at rest ...
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53 views

Is there in quantum physics really a coincidence? [closed]

Coincidence doesn't make a sense in our universe. Something that hasn't any cause of existence just doesn't exist. Even coincidence what computers calculate is not a real coincidence - they calculate ...
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0answers
51 views

1-particle momentum eigenfunction in terms of field operator for real Klein-Gordon field

Suppose $\phi(x)$ is a real Klein-Gordon field, then the single-particle wave function $\psi(x)$ corresponding to a momentum $p$ is given by (QFT, Ryder) $$\psi_p(x)=\langle0|\phi(x)|p\rangle.$$ The ...
3
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2answers
48 views

Is there any difference between massless Dirac fermions and Weyl fermions?

In graphene we call the low energy excitations around the Dirac point Dirac fermions, which are massless. Is this just by convention or is there any further differences between massless Dirac ...
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1answer
25 views

Slit width for minimum spot size in electron slit diffraction if involving uncertainity principle

I don't believe the following is an accurate description of the physical but a homework problem to help understanding. A beam of electron of energy 0.025 eV moving along x-direction, passes ...
1
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3answers
151 views

The need for a 'particle description' of electrons

Is there any phenomenon where the 'wave description' of the electron's motion is not applicable? The reason for this question is to find out if there are any situations were quantum wave theories ...
1
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1answer
27 views

Joint-measure of POVM's

I feel disturbed by this question: Suppose $A$ and $B$ are POVM's with respective $\sigma$-algebras $\mathcal{F}_A$ and $\mathcal{F}_B$ and outcome spaces $\Omega_A$ and $\Omega_B$. Then why can't I ...
4
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1answer
74 views

Why is optical orbital angular momentum (OAM) called “topological charge”?

The terminology "topological charge" is frequent in lots of research papers related to optical vortex or optical OAM, it is used to represent the optical OAM. Why? How to comprehend it?
4
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2answers
160 views

If atoms have specific energy levels, why do opaque solids absorb all visible light, not just some? [duplicate]

Here's my question: if atoms have well defined energy levels and those differences correspond to the frequencies of light that can be absorbed, how is it that opaque objects absorb all or most visible ...
3
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0answers
101 views

Convention in physics for [],{} and operators (QM)

I got a little mixed up with the convention in physics. Usually a hat means an operator. For a given electron-ion Hamiltonian $\hat{H}_{e-n}$, what are the difference between these: 1) ...
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0answers
58 views

What math do I want to focus on for 1) quantum computing and 2) quantum physics? [closed]

What math do I want to focus on for 1) quantum computing and 2) quantum physics? I am interested in studying quantum computing and the Higgs Boson (quantum physics?) and ultimately working in some ...
2
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2answers
66 views

Optical absorption in a semiconductor for $E<E_g$ [duplicate]

Quoting from Solid State Electronic Devices (by Ben G. Streetman and Sanjay Banerjee): A photon with energy less than $E_g$ is unable to excite an electron from the valence band to the ...
1
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1answer
43 views

How and under what principle are measurements made at quantum level? [closed]

There's a lot of news about amazing quantum phenomena, but even without the expert knowledge I would still like to know how it is done and think about the possibility of errors in measurements. How, ...
1
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2answers
64 views

How do we know that photon entanglement isn't the result of the photons's states being predetermined?

I know there is evidence that it is not predetermined and I tried reading articles on it but most of them either don't explain the intuition behind the experiment or they speak in a foreign language ...
2
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0answers
54 views

Are universally valid possibilistic theories possible?

This is a spin-off of the following question: Are Thomas Breuer's subjective decoherence and Scott Aaronson's freebits with knightian freedom the same things in essence? Given that Thomas ...