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-...

learn more… | top users | synonyms (4)

0
votes
0answers
11 views

Is my understanding of creation/annihilation operators' functional dependency correct?

I am trying to gain a little intuition about second quantisation, specifically about creation/annihilation operators. Lets say you quantise the free EM field (in 1d) and end up with the usual: $H=\...
6
votes
8answers
2k views

Prove that an electron in a hydrogen atom doesn't emit radiation [duplicate]

According to electrodynamics, accelerating charged particles emit electromagnetic radiation. I'm asking myself if the electron in an hydrogen atom emits such radiation. In How can one describe ...
54
votes
3answers
7k views

Is it possible to “see” atoms?

As per my knowledge, atoms are small beyond our imaginations. But there is an image on Wikipedia that shows silicon atoms observed at the surface of silicon carbide crystals. The image: How can we ...
-1
votes
1answer
492 views

Dirac Delta Potential and bound/scattered states

Why does the attractive Dirac Delta distribution (function) potential $V = \alpha\delta$(x) (for negative $\alpha$) yield both bound AND scattered states? Is this due to the definition of the Dirac ...
8
votes
4answers
371 views

Curvature of Hilbert space

That may appear as a dumb question, but: Does Hilbert space have curvature, or is it a flat space? How and why?
0
votes
0answers
39 views

How to calculate possible spin of two photon system?

Photon hasn't well defined quantity such as spin. Instead of it, it is characterized by helicity $h$. Let's assume state of two photons in CM frame (with $\mathbf k$ being the momentum of one of ...
-2
votes
0answers
30 views

what is the rough motion of an electron in an atom [duplicate]

If The Uncertainity principle is true,then how does an electron move ?if the motion cannot be random also,then how does it occur?
0
votes
2answers
87 views

Can two different objects or system of molecules have different temperatures, but having same internal kinetic energy?

If I take an extreme case, where a body has only an internal potential energy with zero internal kinetic energy, does this body have a temperature? Another question related to it: if two objects A and ...
0
votes
3answers
98 views

Significance of wave number?

Till now all I know about the wave number is its formula i.e. ${\frac{2\pi}{\lambda}}$. I always wanted to know what it really means. So can anyone please, explain me its physical significance?
0
votes
1answer
36 views

Uncertainty and Classical waves

My professor, introducing Heisenberg uncertainty principle, started from the Fourier transform and the classical uncertainty for waves. He told about the localized impulsive wave $\delta(x)$ which ...
0
votes
2answers
27 views

Understanding Zeeman Splitting

I'm reading a standard modern physics history book ("Inward Bound" by A. Pais), and I realized I don't really understand Zeeman splitting well. In the section I'm reading, there's a short discussion ...
3
votes
1answer
24 views

What happens to the energy of fermions when a degenerate gas forms?

For example, when an electron degenerate gas forms, two electrons (of opposite spins) occupy each of the lowest possible energy states up to the Fermi energy. This is because of the Pauli exclusion ...
-2
votes
0answers
44 views

Expectation value of an Observable and Eigenstates

I am learning about Quantum Mechanics at the moment and I was wondering about Eigenfunctions and Observables. The question I would like to ask is, If a wavefunction is not an eigenstate of an ...
-1
votes
0answers
37 views

This might make no sense light is time [on hold]

I've done a lot of research on time I think when light/color is absorbed it is giving off as time and when it is going fast the light can't keep up
1
vote
2answers
163 views

Quantum probability of entangled spin-1/2 particles?

Let us say that you have two entangled spin-1/2 particles (entangled in such a away that angular momentum is conserved). Let us say particle 1 moves to the left and particle 2 to the right. We measure ...
0
votes
1answer
118 views

Reduced density matrix

During a course on quantum mechanics we've been talking about density matrices. Now I came across the following exercise. Consider a two spin $\frac{1}{2}$ systems, labeled 1 and 2. Calculate: ...
3
votes
3answers
176 views

Is my understanding of the delayed choice quantum eraser correct?

I'll say in advance that I am by no means an expert on Quantum Mechanics. I understand the basic mathematics of it (Wave function and Schrodinger equation), but did not go deeply into it or study it ...
5
votes
1answer
65 views

One particle states in an interacting theory

Question: What is the general definition of one particle states $|\vec p\rangle$ in an interacting QFT? By general I mean non-perturbative and non-asymptotic. Context. 1) For example, in Weigand'...
2
votes
2answers
88 views

The meaning of 'coupling'?

In quantum mechanics if two quantities $A$ and $B$ are said to be coupled what does this actually mean? I would guess that it means we have a term like $A\cdot B$ in the Hamiltonian but this is only ...
3
votes
1answer
135 views

A question on the Chern number and the winding number?

Let $\mid \psi(x,y) \rangle$ be a normalized wavefunction living in a $d$-dimensional Hilbert space and depend on two real parameters $(x,y)$ that belong to a closed surface (e.g., $S^2, T^2$, ...). ...
2
votes
0answers
47 views

$\left< \frac{\partial (xp)}{\partial t} \right> = 0$ When is this true?

Is this always true in quantum mechanics? $$\left< \frac{\partial (xp)}{\partial t} \right> = 0$$ I encountered this when working problem 3.31 in Griffiths Introduction to Quantum Mechanics II....
0
votes
0answers
15 views

Why must the separation constant be real in a time dependent wave function?

I'm not sure if I'm asking this right. I'm reading ''Introduction to Quantum Mechanics'' by Griffiths and in the chapter 2 exercises he asks to prove that the separation constant, $E$, must be real. ...
4
votes
2answers
362 views

Off-diagonal elements of Hamiltonian matrix $H_{12}$ & $H_{21}$: energy of transition from $|1\rangle$ to $|2\rangle$ or amplitude of transition?

$$ \newcommand{\k}[1]{\left| #1 \right\rangle} \newcommand{\dd}[1]{\frac{d #1}{dt}} $$ In a Hamiltonian Matrix like this: $$H = \begin{pmatrix} E_{11} & E_{12} \\ E_{21} & E_{22} \end{...
0
votes
3answers
183 views

Treating matter waves as light waves?

Is it valid to treat a matter wave as a light wave with wavelength equal to the de Broglie wavelength of the matter wave? Either way please can you explain why?
1
vote
1answer
65 views

Is the MWI symmetric in time?

Reading the blog of Sean Carroll (I recognize he isn't the only voice) has made me more sympathetic to the notion of many worlds, but reading Susskind (also not the only voice) has made me think that ...
-6
votes
0answers
32 views

quantum mechanics problem orthonormal function [on hold]

$$\psi_n(x)=\sqrt{\frac{2}{a}}\sin\left(\frac{\pi n}{a}x\right)$$ is this wave function orthonormal or not? If yes then prove it.
0
votes
1answer
65 views

Practical way of expressing the $\delta$-function [on hold]

I have got a problem in using the $\delta$-function. As we know, this function is often used to define a 'density'-related quantity. Such as the density of states or some correlation function. Take ...
14
votes
1answer
283 views

Do Franck-Condon oscillations have natural lineshapes?

I recently found a paper (for the curious, this one) that talks about observing the motion of a nuclear wavepacket in H2O, as initiated by tunnel ionization. This wavepacket should be thought of as a ...
2
votes
3answers
57 views

Two qubits system in polar co-ordinates

I know that I can write a single qubit state in terms of polar co-ordinates $(r,\theta,\phi)$ on a Bloch sphere. \begin{equation} \rho = \begin{pmatrix} \frac{1+r \cos\theta}{2} &\frac{r \exp(-i\...
3
votes
1answer
147 views

Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
4
votes
2answers
752 views

What causes Potassium to decay into Argon the way it does

From evolutionwiki: "Potassium 40 decays into argon 40 through a process known as electron capture. In electron capture, an electron from the innermost electron shell "falls" into the nucleus, ...
11
votes
1answer
234 views

Significance of the exception to Gleason's Theorem when n = 2

Gleason's Theorem famously asserts that (appropriately defined) measures on the lattice of a complex Hilbert space can be implemented by density operators via the trace operation, except in the case ...
-4
votes
2answers
47 views

How to resolve “bottleneck” of encoding input of quantum computer? [on hold]

As far as I understand, all quantum computing purpose is to accelerate exponentially (upon input length) computation time of given task. But here user faces bottleneck to serialize input, and ...
12
votes
1answer
373 views
+50

Does measurement, quantum in particular, always increase the total entropy?

Measurement of a quantum observable (in an appropriate, old-fashioned sense) necessarily involves coupling to a system with a macroscopically large number of degrees of freedom. Entanglement with this ...
3
votes
1answer
50 views

On LOCC operations

I am trying to learn quantum information theory. Suppose we have a bipartite (as well as multi-partite) quantum system $H_A \otimes H_B$. What is a LOCC map $\phi: \mathcal{B}(H_A \otimes H_B) \...
1
vote
0answers
40 views

Are Fock spaces just a special type of tensor algebra?

Are Fock spaces just a special type of tensor algebra? The definitions I am using: http://en.wikipedia.org/wiki/Fock_space http://en.wikipedia.org/wiki/Tensor_algebra From what I can tell, the ...
5
votes
1answer
144 views

How to calculate the ground states' Berry phases with doubly degeneracy, such as that due to the particle-hole symmetry or time reversal symmetry?

Suppose the ground states of a system are doubly degenerate due to an anti-unitary symmetry $K$, which are $|\psi>$ and $|K\psi>$. If the system is an one-dimensional Fermion system and anti-...
0
votes
0answers
33 views

Eigenkets in matrix representation [on hold]

We use base kets in matrix representation of an operator $X$. Could the base kets be possibly be eigenkets also, of operator X? (Here, I'm taking X as a general operator , not only observable,i.e. ...
9
votes
2answers
3k views

Do protons exchange photons with electrons?

I'm sorry for this question but, I just don't get it. According to the electromagnetic field theory, electrons repel each other by exchanging photons. How do protons attract electrons, by photon ...
0
votes
3answers
554 views

Quantum Mechanics in Electric Field

I am working on a problem which looks like this. Consider a charged particle with charge $q$ trapped in a box of length $L$ with finite constant potential $ V_0 $ on both ends. A constant (static) ...
-5
votes
1answer
43 views

Communication via teleportation/entanglement (FTL communication)

I know this has been asked many times, but I have a hard time "crystallising" it in my mind. First: let's say we teleport a DVD (with quantum teleportation). Isn't this FTL communication? Second: ...
0
votes
0answers
43 views

How to do partial trace of three qubit? [closed]

Good day, $\|A\rangle=\left(\dfrac{i_0}{j_1}\right)$, $\|B\rangle=\left(\dfrac{i_0}{j_1}\right)$, $\|C\rangle=\left(\frac{i_0}{j_1}\right)$, For 2-qubit systems, the $\|AB\rangle\langle AB|$, ...
8
votes
1answer
691 views

Many-worlds: Where does the energy come from?

With regard to the theory that each time a wave function collapses the universe splits so that each possible outcome really exists - where does all the energy required to create all the new universes ...
2
votes
2answers
127 views

What is the correct quantization of Hamiltonians of the form $H=x·p$ whose naive quantization is not Hermitian?

As we all learn in Basic Quantum Mechanics (the first quantization), we promote the classical variables to operators. Say, the classical hamiltonian $\frac{p^2}{2m}+V(x)$ to $-\frac{\hbar^2}{2m}\frac{...
2
votes
1answer
140 views

Thermionic emission, delayed emission and predissociation

In molecular photodissociation, the thermionic emission, delayed emission and predissociation are the same? Otherwise, what is the difference between them? My question is not about the solids, but I ...
0
votes
0answers
27 views

Balancing a Quantum mechanical pencil [duplicate]

I have tried to solve the question given in Sakurai quantum mechanics book about what is the maximum time you can balance a pencil on its tip using the uncertainty principle. Classical pencil is in ...
1
vote
1answer
131 views

Excitation energy of carotene using the particle in a box model

I'm practicing for an exam and I came across the following question: The linear, conjugated π-electron system of a carotene molecule comprises 11 atoms and the distance between two atoms is 1.4 Å. ...
5
votes
2answers
83 views

Uncertainty Relations, Conjugate Quantities, and Fourier Transforms

I've heard from a lot of people that the reason momentum and position have an uncertainty relation is because of the Fourier Transform. But is this in any way the case? If it were I would expect all ...
1
vote
2answers
168 views

Does quantum randomness measurably affect macro-sized objects?

I understand that while it is believed that there is no true randomness on the macro scale, there is true randomness on the quantum scale. A previous theory that quantum processes could be determined ...