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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1answer
64 views

Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation ...
7
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0answers
95 views

Role of physics in the zeta function $\zeta$ and the Riemann hypothesis

Hilbert and Polya suggested a physical way to verify the Riemann hypotesis about $\zeta(x)$. If the Riemann hypotesis is true, we can state all eigenvalues of physical problems are real. What is the ...
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0answers
29 views

preparing qutrit mixed state

I have a problem: Ok so I want to create a superposition qutrit state, like this: $$ |\Psi\rangle=\frac{1}{\sqrt{3}}(|0\rangle+|1\rangle+|-1\rangle) $$ is it possible to go there, starting with an ...
3
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1answer
78 views

Is there some quantum potential producing exponential eigenvalues?

Usual central potentials produce quantum spectra with energy levels going as $n$, $n^2$, $n^3$ and so on, being $n$ the quantum number of the orbit. In the other extreme we have "dirac-delta" ...
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0answers
6 views

Spatial Resolution in Magnetocardiography

In the science paper called Development of an optical cardio-magnetometer by George Bison, it is mentioned that spatial resolution of 10-20mm is required for mapping MCG signal(page 52). What does the ...
4
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0answers
43 views

Is it possible to construct a quantum “computer” using laser light similar to the double-slit experiment?

Is it possible to construct an arrangement of optical devices (lasers, mirrors, slits, splitters) such that the construction could carry out a single quantum "computation"? I understand that such a ...
7
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4answers
217 views

Does Heisenberg equation of motion imply the Schrodinger equation for evolution operator?

Let us choose to postulate (e.g. considering the analogy of the Hamiltonian being a generator of time evolution in classical mechanics) $$ i\hbar \frac{d\hat{U}}{dt}=\hat{H}\hat{U}\tag{1} $$ where ...
2
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1answer
50 views

Formalism and representation in Quantum Mechanics

I am just curious about the formalism of basic Quantum Mechanics. Lets take for instance the system of a spin-$\frac{1}{2}$ particle. The state of the particle is described by a vector in an abstract ...
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2answers
72 views

Idempotent Operators

If $P$ is an idempotent operator, $P^2 = P$ and we have a vector $|\psi\rangle$, $P\neq1$, and the relation $$PL |\psi\rangle = L|\psi\rangle,$$ what conclusions can we draw about $L$, which is a ...
0
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1answer
45 views

Are only 2 bits of information transmitted in quantum teleportation?

Prompted by the recent success in Delft, I've been reading a number of papers and articles about quantum teleportation. I'm comfortable with my understanding of most aspects but haven't found much ...
0
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1answer
29 views

Is a lightlike vector potential (A²=0) a valid and/or useful choice?

I know most common choices to fix the gauge of a vector potential, but I wonder if there are no other choices possible. As a concrete example inspired by the Schrödinger equation with magnetic field, ...
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0answers
24 views

Computational package to find the ground state of a particle in 3D domain

I am developing a numerical algorithm to find the ground state of a Hermitian matrix. Obvious applications are quantum many-body systems and particles in various potentials. I am a little stuck with ...
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3answers
76 views

Solving the Schrödinger equation where the initial wave function is an energy eigenfunction

I was watching Allan Adams' lecture on energy eigenfunctions, and there's one part (around 43 minutes into the lecture) that confuses me. Suppose we have the initial wave function $\Psi (x,0)$ such ...
20
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4answers
2k views

Which Is More Fundamental, Fields or Particles?

I hope that I am using appropriate terminology. My confusion about Quantum Theory (beyond my obvious unfamiliarity with its terminology) is basically twofold: 1) I lack an adequate understanding of ...
2
votes
1answer
114 views

How to explain in simple terms why Entanglement is more than just complicated hidden variables

I haven't taken a graduate level physics course on quantum mechanics so I get lost in the strange looking equasions. It's hard for me too see in any of the explanations of how quantum computers and ...
0
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1answer
42 views

Trying to measure travel time of photons in a double slit experiment

So far I'm only tasting the quantum mechanics. Haven't gone very deep into the mathematics of it yet. I read about the double slit experiment, and the weird consequences of it: if you put a detector ...
2
votes
1answer
100 views

From where randomness comes from and why it exists? [closed]

I recently began to study statistics and probability and I have two questions: Where does randomness come from? What is the source of randomness? Why does the randomness exist? Is it possible to ...
1
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1answer
33 views

Time dependency of the phase of a single photon

I am wondering if a wave packet of a single photon in the time domaine $$ \psi(t)=|\psi(t)|\; \text e^{\text i \varphi(t)} $$ can have a different $t$ dependence in phase than the simple phase ...
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0answers
58 views

Quantum mechanics and probability

I've done an intro course on QM and I'm now hoping to understand exactly how to use probability theory rigorously in solving problems. My question is: How do I do the same thing, or the closest thing ...
0
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2answers
40 views

Dual particle-wave behavior

If electrons and photons, and possibly more particles, exhibit dual character, why don't physicists create a new classification for them? Why describe them as both waves and particles. Why not rather ...
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2answers
41 views

Modeling Quantum Aspects with Probability

This is a question I've had a while about quantum theory. Many times when I look at books and equations about this subject matter I see that the use many concepts in probability. (Correct me if Im ...
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3answers
160 views

The boundary for quantum mechanical behavior and classical mechanical behavior

To what size and how does "quantum weirdness" such as entanglement and superposition stop applying to larger objects (mere unions of these quantum particles). How do these macro objects that behave as ...
0
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1answer
49 views

What are some publications which continue Schrödinger's “What is life?” discussion?

I'm looking for modern publications on the physical nature of life in which the primary reference is to the discussion started by Schrödinger in 1944 in his book "What is life". For example, ...
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2answers
50 views

What is the energy operator and from where do we get it?

I am trying to learn Quantum mechanics from MIT OCW Videos about quantum mechanics. I have reached the 5th lecture. Please help me in understanding this: In the middle (At 32:08), the professor wrote ...
1
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1answer
71 views

How can one calculate the phase difference between two quantum harmonic oscillator (Hermite-Gauss) states?

The analytic solutions of a quantum harmonic oscillator are given by Hermite-Gauss states, which differ in the order $n$ of the Hermite polynomials. If two such states are plotted, there will be a ...
4
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0answers
30 views

How to distinguish Bose glass and superfluid phases in a harmonic trap?

In mean-field study of Bose-Hubbard model in an optical lattice, what parameter can be calculated to distinguish Bose glass and superfluid in a harmonic trap?
5
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1answer
67 views

What does the Higgs boson have to do with the uncertainty principle and quantum oscillations?

I was looking in New Scientist the other day when I saw something to do with the Higgs boson, energy levels, entropy, space/time, quantum oscillations and many other things. It was in a feature to do ...
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1answer
73 views

Quantum Mechanics and Entanglement

I'm hearing a guy ( Tom Cassidy ), which supposedly has a master in physics, saying that what we expect in a physical experiment ( for example, observing some particle ) can actually interefere with ...
0
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1answer
44 views

What is the cut-off for quantum superposition?

Is there an explanation as to how macro objects aren't in superposition? At what size do objects stop being in a state of superposition?
4
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3answers
262 views

Quantum Mechanics or Classical Mechanics? [closed]

I'm just a student of grade 11 but, I was interested in knowing about Physics much deeper. In order to start my interest in Physics, I watched this video of Quantum Physics NOVA : Quantum ...
1
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1answer
36 views

Sign of the wave function in orbital representation?

I have some fog in my head and a rather simple question for you: When the sign of the wave function is representated on orbitals, what is this sign? I mean is it the sign of the real part of the ...
2
votes
1answer
28 views

Linearity of the time evolution operator for the reduced density matrix of an entangled state

Suppose to have a system $S$ immersed in an enviroment; the pure states are elements of $H_S \otimes H_E$, where $H_S$ is the hilbert space of the system and $H_E$ is the hilbert space of the ...
1
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1answer
80 views

I am trying to calculate how $<r>$ in the hydrogen atom evolves with time

I am working on the Hydrogen atom and I was trying to calculate $\frac{d<r>}{dt}$ using $$\frac{d<r>}{dt} = \frac{i}{\hbar} <[\hat{H} , \hat{r}]>.$$ Here $r = \sqrt(x^2 + y^2 + z^2)$ ...
1
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1answer
89 views

Infinite-dimensional Hilbert spaces in physical systems

Can anyone give an example of when infinite-dimensional Hilbert spaces are required to describe a physical system? The standard answer to this question is yes, and I'm sure some of you will be quick ...
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votes
2answers
53 views

Energy carried by photon not conserved?

In an imaginary frame of reference traveling with a photon, the length of the path traveled is 0. If the length of the path is 0, isn't it similar to say that the photon is either at the source or at ...
1
vote
2answers
103 views

Has a photon or electron ever been observed in a state of superposition?

Has subatomic particles ever been seen in a state of superposition or do we just detect information like qubits about the state of the particle? So is actual matter in superposition or is it just ...
3
votes
1answer
67 views

Two-level system with spontaneous emission

I have been stuck with this elementary problem of two-level system including spontaneous decay. After solving by standard procedure the following pair of equations, when I plot the expressions of the ...
10
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1answer
461 views

Interpretations of quantum mechanics

It is well known that there are many interpretations of quantum mechanics. I'm wondering if there is a specific reason why the Copenhagen interpretation is the most popular. Why is it that the ...
1
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0answers
54 views

What is the right way to learn quantum physics? [closed]

So I have a question about what i should do with my path to learning quantum physics. I just have no idea where to start or to continue from where I left off. I have been studying quantum mechanics ...
4
votes
1answer
89 views

Why is string theory a two dimensional quantum (conformal) field theory on its worldsheet?

In string theory, we quantize the two dimensional field theory on the string's worldsheet. I have a question about this kind of quantization of string theory: did we have similar theory for point-like ...
3
votes
1answer
71 views

Poles for a particle scattered in a delta potential

I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also ...
1
vote
1answer
49 views

How is a photon/particle measured when passing through one of the slits of the Double Slit Experiment?

It is stated in many popular science videos that one of the reasons that quantum mechanics is so wacky is that if you measure which slit the photon/particle went through on the way, then you no longer ...
1
vote
1answer
63 views

Why do some bound states disappear in a discontinuous way?

Generally, we have the picture that as the parameter (say, the depth of a trap) of a system varies, the bound state gets more and more extended and disappears eventually at some critical parameter ...
0
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0answers
24 views

Stochastic process corresponding to Schrödinger evolution

In probability theory, the Fokker-Planck equations governs the trajectory of a sample path of a stochastic process -- say the heat equation in the case of a Wiener process. Consider a Gaussian ...
1
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3answers
85 views

Can the distance over time of an electron between two measurements be higher than the speed of light?

So measure an electron, take down it's position $p$. Then measure the electron a second time and take down it's new position $p'$. Note the time between measurements, $t$. What does physics say about ...
0
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2answers
114 views

Does processing for a quantum computer take place in other universes?

Apologies in advance if my question seems misinformed. I am a software developer, and neither quantum mechanics nor physics are my specialties. From ...
0
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1answer
103 views

Problem in Grandfather paradox

I am very confused about a paradox and a recent research on Quantum particles. I have read an article which states that time travel is possible for quantum particles. If it is possible then why does ...
9
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2answers
194 views

Deriving the expectation of $[\hat X,\hat H]$

For a free particle of mass $m$, with Hamiltonian $$\hat{H} = \frac {\hat{P}^2} {2m},$$ where $$\hat{P} = -i \hbar \frac{\partial} {\partial x}.$$ The commutative relation is given by $$[\hat{X}, ...
0
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1answer
84 views

Matrix elements of the operator $\hat{x} \hat{p}$ in position and momentum basis

I want to calculate the matrix elements of the operator $\hat{x} \hat{p}$ in momentum and position basis, that is the two quantities ($p,q$ - momenta, $x,y$ - positions): $$\langle p|\hat{x} ...
0
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0answers
36 views

A crash course in quantum mechanics [duplicate]

I am shortly due to begin a summer project lasting roughly 6 weeks with the aim of performing some relatively basic calculations in the theory of open quantum systems. However, at this stage in my ...