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 quantum-field-...

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57 views

On a measurement level, is quantum mechanics a deterministic theory or a probability theory?

Quantum mechanics is a non-commutative probability theory. As such, it fundamentally behaves differently from classical probability theories. This manifests itself most pronouncedly in the uncertainty ...
2
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1answer
39 views

Express state as eigenkets

this is very basic but I just suddenly confused. Since any state can be expressed as complete set of eigenkets with discrete eigenvalues $$|P\rangle = \sum^n c_n |p_n\rangle$$ I understand above. But ...
5
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0answers
45 views

Can this relativistic hack allow one to see beyond an event horizon, in principle, else why not?

Consider a lone photon. As its frequency increases, its energy increases. Taken to the limit, a sufficiently-high-frequency photon could be a black hole unto itself. But the frequency of a photon is ...
2
votes
2answers
42 views

Two particles system

Source: http://www.youtube.com/watch?v=k3K_lyvbfOE For two particles system(09:30), why is it wave function a product of each particle's wave function? E.g.$$\psi(x_1,x_2)=\psi_a(x_1)\psi_b(x_2)$$ ...
0
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0answers
25 views

When should parameters be replaced while changing basis?

I have the following equality: $$a\lvert 00\rangle + b\lvert 11\rangle = a\lvert ++\rangle + b\lvert --\rangle$$ for any $a,b \in C$ that satisfy the normalization condition. For $a = \frac{1}{\...
0
votes
1answer
28 views

Proper definition of the Wannier function

I am studying the construction of the Wannier functions for 1D system with periodic boundary conditions and my reasoning seems to be a little bit different from what I can find in textbooks. First ...
3
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0answers
34 views

Zeno effect in quantum gravity?

Given that "the quantum zeno effect can "freeze" the evolution of the system by measuring it frequently enough in its known initial state." Is there any equivalent/similar Zeno effect in quantum ...
0
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0answers
14 views

States after measurement

I am learing about quantum mechanics, and I am quite unclear about the the role of measurement and the density operator. Let $\mathcal H$ be a Hilbert space, $\psi(t) \in \mathcal H$, $O$ be a ...
1
vote
0answers
130 views

Lindblad equation derivation

I'm reading A simple derivation of the Lindblad equation. It introduces a Hamiltonian for a system consisting of a principal system $S$, a heat bath $B$ and an interaction term: $\hat{H}=\hat{H}_S+\...
1
vote
3answers
297 views

Can we predict throwing a dice?

What happens if we throw a dice from same position, with same force, by creating a vacuum environment on earth? Will it be predictable now i.e. will the dice have same results all the time? If answer ...
3
votes
1answer
105 views

Is it possible to synthesize an EMW which is not quantized?

( I initially started to ask, "since according to Quantum-theory of light; the energy of a photon, depends only on the frequency of light-wave (E = h * nu), and no-mention of amplitude. So, does the ...
1
vote
2answers
40 views

Why is the energy expressed in an electron orbital change of state electromagnetic (photon)? [on hold]

As I understand, Schrodinger's wave equation predicts the allowable energy states an electron can have under the electromagnetic forces of a given nucleus (and I assume other 'orbital' electrons). If ...
2
votes
1answer
167 views

Feynman's derivation of the Schrödinger equation

I'm reading the following article: Feynman's derivation of the Schrödinger equation In this article, the autor claims that Feynman derivation of the Schrödinger equation was a key aspect of the ...
2
votes
0answers
38 views

Energy Spectrum and Gauge Transformations

There is a question in SE about the fact that the Hamiltonian isn't invariant under the EM gauge transformations. I wanted to ask about its consequences here. I know that in general, the Hamiltonian ...
1
vote
1answer
36 views

Free particle Schrodinger equation: propagator

I am going through Shankar's Principles of Quantum Mechanics and am having trouble finding the free particle propagator $U(t)$ that satisfies $\lvert\psi (t)\rangle = U(t)\lvert\psi (0)\rangle$ due to ...
-1
votes
0answers
19 views

What's role of signal-to-noise ratio in the quantum measurement? [on hold]

Recently, I've been watching videos of MIT opencourse (http://www.youtube.com/watch?v=TcvY8Nt0ZGA&list=PLUl4u3cNGP62FPGcyFJkzhqq9c5cHCK32&index=2) taught by Nobel laureate Wolfgang Ketterle. ...
13
votes
4answers
428 views

Is it possible to reconstruct the Hamiltonian from knowledge of its ground state wave function?

Is it possible to "construct" the Hamiltonian of a system if its ground state wave function (or functional) is known? I understand one should not expect this to be generically true since the ...
3
votes
1answer
48 views

Is the single slit experiment a practical example of Heisenberg's uncertainty principle?

I saw some videos where a person points a laser through a slit. As they reduce the width of the slit, the diffracted image spreads out, like this: Can this pattern be viewed as a consequence of ...
3
votes
1answer
141 views

How force get transmitted when a magnet attracts iron?

According to particle physics , every fundamental force has its force carrier particle. Photon is a force carrier particle of electromagnetic force but how does force gets transmitted when a iron is ...
1
vote
0answers
27 views

Minimum gap between consecutive energy levels?

Assume a standard one-particle, non-relativistic Hamiltonian of the form \begin{equation} H=\frac{p^2}{2m}+V(r) \end{equation} and denote its eigenvalues as $E_{n,\tau}$, where $n$ is the principal ...
-3
votes
1answer
46 views

Simplest way to store a quantum superposition temporarily [on hold]

My understanding of the Schroedinger's Cat experiment is that, while it's an amusing thought experiment, the cat would not actually be in a superposition of states because it's just too massive an ...
3
votes
1answer
472 views

How does an operator transform under time reversal?

We know that a time-reversal operator $T$ can be represented as $$T=UK$$ where $U$ is some unitary operator and $K$ is the complex conjugation operator. Then under time-reversal operation, a quantum ...
-6
votes
0answers
57 views

What am I missing on my thougth expierement? [on hold]

Before I say my thought experiment I wanted to state that most of my knowledge on physics and such is from college books, and not from actual instruction. I arrived at this conclusion and realized I ...
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votes
2answers
55 views

Possiblity for particle to be carried by a wave such as a photon or electromagnetic wave/waves in general for means of transportation/travel? [closed]

I am wondering whether it is possible for a photon/EM wave to carry a very small particle like an elementary particle or smaller on it like a highway carries a car traveling on the highway or an ocean ...
0
votes
0answers
10 views

Switching Parity in a Superconductor

I've got a pretty simple question that's been bothering me for a while. This is the issue. Suppose we have a superconductor with phase $\phi$, and we change this to $\phi+2\pi$. One would think that ...
-8
votes
1answer
50 views

Doesn't quantum uncertainty disprove string theory? [duplicate]

String theory states that the oscillations of little strings are responsible for all the particles in and the evolution of the universe. The specific type of particle created by a string depends on ...
1
vote
1answer
78 views

Why don't the internal electric and nuclear forces holding atoms and molecules together cause decoherence during a buckyball double-slit experiment? [on hold]

My understanding is that anything that qualifies as an "observation" or "measurement" will cause the "fuzziness" of the superposition to disappear to the local observer, and the results of said ...
1
vote
1answer
118 views

Direct Sum representation of multiple particles in Quantum Mechanics

Suppose that I have three non-interacting spin-1/2 particles such that I can represent the combined system in a basis of \begin{align} D^{(1/2)}_1 \otimes D^{(1/2)}_2 \otimes D^{(1/2)}_3 & =(D^{(...
0
votes
2answers
66 views

Completeness relation for coherent states of the quantum harmonic oscillator

For the Quantum harmonic oscillator with energy eigenstates $|n\rangle$ one defines a coherent state for every complex number $z$ by setting (note that the normalization varies across the literature) $...
0
votes
1answer
23 views

Corrections to the Bohr energies of Hydrogen [on hold]

Among fine structure, Hyperfine splitting and Lamb shift, why Hyperfine splitting is the smallest while Fine structure is the largest?
2
votes
3answers
87 views

Bell inequality violations evidence for 1935 EPR claims?

Is it possible that Bell inequality tests provide experimental evidence in support for the EPR claims in their 1935 paper titled "Can Quantum-Mechanical Description of Physical Reality Be Considered ...
3
votes
1answer
534 views

Wigner Threshold law in Photodetachment and Photoionization

I am writing this question here because I have a problem in understanding the Wigner Threshold law in Photodetachment and Photoionization. The Wigner Threshold Law is given by: $\sigma$=$E^{L+1/2}$. ...
0
votes
1answer
194 views

What is the form of the kinetic energy operator on a one-dimensional (real space) lattice? (In second quantization)

I'm trying to figure out how one would write down the Hamiltonian of a free fermion system (eventually in second quantization) on a one dimensional lattice and I'm having trouble both coming up with ...
7
votes
1answer
203 views

Uncertainty relation for non-simultaneous observation

Heisenberg's uncertainty relation in the Robertson-Schroedinger formulation is written as, $$\sigma_A^2 \sigma_B^2 \geq |\frac{1}{2} \langle\{\hat A, \hat B\}\rangle -\langle \hat A\rangle\langle \...
3
votes
2answers
2k views

Changes in Water Bonding Angle

I heard something recently in a casual discussion, but have yet to be able to confirm it: is there any evidence that the bonding angle for a water molecule, currently defined as 104.5, has been either ...
1
vote
1answer
47 views

What happens to the visible light that a substance does not reflect on an atomic level?

Let's say we have a blue, opaque material. If white light was incident on that material, the blue light would be absorbed by electrons and the electrons would transition to a higher energy state, and ...
-1
votes
2answers
70 views

Why don't electrons moving around in a orbit produce electromagnetic waves in their natural state? [duplicate]

If moving electrons produce changing electric field, and if changing electric field produces magnetic field, every electron must produce an electromagnetic wave. This means an atom in its natural ...
2
votes
0answers
27 views

Degeneracy of energy levels of a particle in a spherical step potential?

I have a particle of mass $m$ and spin $1/2$, in a spherical step potential, $$ V(r) = \begin{cases} 0 & r<a, \\ V_0 & r>a. \end{cases} $$ Now they ask me to find, without solving the ...
0
votes
0answers
45 views

Entanglement of bi- and tripartite pure and mixed states

since I'm not sure on how to find out whether a system is entangled or not I thought about examples that could clarify the whole thing. first example: system is in the state $\rho=1/2 (| 000 \rangle \...
1
vote
0answers
42 views

Trouble understanding Nielsen & Chuang exercise

I am probably just stuck on something very simple, but I'm having trouble understanding a premise of Exercise 10.40 in Nielsen & Chuang. The full details of the exercise are not important for my ...
6
votes
3answers
793 views

Entanglement, Bohr-Einstein Debate, Bell's Inequality

On BBC episode The Secrets of Quantum Physics (Part 1) Jim Al-Khalili explains quantum mechanics for the layman. In the first half, he does a very good job; in the second half, either he thought his ...
-5
votes
0answers
40 views

Why is the Heisenberg uncertainty priciple considered as a universal truth? [duplicate]

You should have heard about Heisenberg and his uncertainty principle. I want to know why it is considered as a universal truth, and not a technological limitation. I'd prefer an elaborate answer with ...
3
votes
3answers
288 views

Dummy variables in Dyson series

In the Dyson series, it is known that: \begin{align} {\cal T}\exp\left[-\frac{i}{\hbar}\int_0^tH(t')dt'\right] &= I - \frac{i}{\hbar} \int_{0}^{t} dt' H(t') + \left(-\frac{i}{\hbar}\right)^2 \...
-2
votes
0answers
24 views

Imaginary part in calculation [closed]

I want to simulate (I use mathematica) a matrix that has imaginary number. Given the matrix, $$A = \begin{pmatrix} e^{2I+3}Sin{(2\Pi t)} & e^{I (\Pi)}Cos{(2\Pi t)} \\ Cos{(2\Pi t)} & -e^{...
14
votes
4answers
679 views

Increasing a potential causes increase in energy levels

Suppose a potential $V(x)$, and suppose a bound particle so the allowed energy levels are discrete. Suppose a second potential $\widetilde{V}(x)$ such that $\widetilde{V}(x) \geq V(x)$ for all $x$ (...
1
vote
1answer
54 views

Using the momentum-space definition of the position operator in position space?

For the position operator $\hat X$: $\hat X \rightarrow x$ in position space $\hat X \rightarrow i \frac{\partial}{\partial k_x}$ in momentum space Question: Can $\hat X \rightarrow i \frac{\...
3
votes
1answer
69 views

Problem with figuring out sign conventions in QFT

I have a problem with sign conventions in QFT which I have trouble dealing with myself. I self-study and mainly use Weinberg and Peskin. I will present the reasoning following conventions adapted by ...
0
votes
0answers
34 views

Systems with extensive ground state degeneracy

This is sort of a follow up to this question: What does it mean for a Hamiltonian or system to be gapped or gapless? There it is stated in one of the answers that a system is gapped if it fulfills ...
4
votes
1answer
229 views

Proving that Measurement increases von Neumann entropy [on hold]

Let $V$ be a finite dimensional complex inner product space. Let $\mathcal{M}$ be the classical sample space of measurement outcomes that may occur in a given experiment, and $M_\mu$, $\mu \in \...
-2
votes
0answers
42 views

Problems on rectangular well [on hold]

We have a rectangular potential well from $x=-b$ to $x=a$.Can we divide the well into two parts from $x=-b$ to $0$ and $x=0$ to $a$ to solve Schrodinger equation?Actually,I want to know how to solve ...