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 ...

learn more… | top users | synonyms (4)

0
votes
1answer
51 views

Do subatomic particles have dimensions?

We know atoms are mostly "made" out of empty space, so the nucleus and all the subatomic particle are very small in compared to the magnitude of the atoms. We also know that atoms are incredibly ...
0
votes
0answers
27 views

Difference between apply quantum gate and measure a qubit?

When you apply a quantum gate, why does the superposition state not collapse? Does this in any way intervene with the qubit as in the measurement?
0
votes
1answer
38 views

Do all quantum systems have zero point energy ?

I understand that it is possible to write an uncertainty relation between the Hamiltonian of a system and time, where the time uncertainity is defined by the amount of time it takes an arbitrary ...
0
votes
0answers
23 views

How do I find the electron confinement energies in a spherical quantum dot?

So if I've got a spherical quantum dot, we'll say it has a 10nm diameter for simplicity. This dot is a semiconductor and it has an electron with an effective mass altered by a factor of 0.2. How do I ...
1
vote
1answer
75 views

Quantum Mechanics Notation

Generally we have that $$|\psi\rangle=\int_{all space} \psi(\mathbf x)|\mathbf x\rangle d^3\mathbf x$$ and therefore $\psi(\mathbf x)=\langle\mathbf x|\psi\rangle$. When discussing the mutual ...
0
votes
1answer
29 views

Normalisation of simple wave function [closed]

I'm currently hanging on a simple normalization of following wave function: $$\psi_1(x)=N_1\exp(-\frac{(x-a)^2}{4a^2}),$$ where $N_1$ is the normalization factor to get, and $a\in \mathbb{R}$ ...
-3
votes
2answers
64 views

Classical notion of trajectory [on hold]

Why the classical notion of trajectory is meaningless in quantum mechanics? I am asking here about notion of trajectory from classical mechanics and why in quantum mechanics we cannot use it or is ...
-2
votes
1answer
33 views

Using creation and annihilation operators to prove the expression for the $n$th excited state in terms of the vacuum state

How does one prove that the $n^{th}$ excited state of a quantum harmonic oscillator (QHO) can be obtained by applying the creation operator $a^{\dagger}$ $n$-times to the vacuum state $\vert ...
1
vote
1answer
45 views

Derivation of Interaction energy of Dipole - Induced Dipole Interaction

I see that the formula giving the potential (interaction) energy of a dipole and an induced dipole is $$V=-\frac{C}{r^6}$$ where $$C=\frac{\mu_1^2 \alpha'_2}{4 \pi \epsilon_0}$$ and that the formula ...
0
votes
0answers
26 views

Strong and Weak limits in Quantum Mechanics

What are strong and weak limits in Quantum Mechanics ? especially in the terms of scattering theory and Moller operators ? References to some standard book will be appreciated.
0
votes
1answer
81 views

Quantum mechanical tunneling

Keeping extraneous ideas and postulates to a minimum, How can we explain the process of quantum-mechanical tunneling?
3
votes
1answer
52 views

How are the PPT criterion and Bell's inequality different?

Bell (1964) writes that if we assume an equivalent classical hidden variable distribution for a two-qubit state then the expectation value of the product of two observables $A$ and $B$ can be written ...
0
votes
1answer
40 views

What is the meaning of “site”?

Reading questions, I have come across a recurring notion of "site". Whilst I am able to understand the questions I am unsure as to what a "site" actually is and to what it corresponds physically. I ...
3
votes
1answer
52 views

Evolution of Eigenstates when two spin systems are coupled

I would like to describe the following situation: We have two spin systems: Spin 1 ($S_1$) and Spin 1/2 ($S_2$). Now imagine you somehow change their interaction so that you can finetune the ...
7
votes
1answer
293 views

Do electrons oscillate into muons just like electron-neutrinos into muon-neutrinos?

And if not, why? What is the difference to neutrinos oscillations?
3
votes
1answer
55 views

Eigenvectors of $p_x$ in a particular domain

Defining the $p_x$ operator for the problem of particle in a infinite well. In the book by Capri on Quantum mechanics, the domain of the operator is given by, $$ p = -i\hbar \frac{\partial ...
0
votes
1answer
25 views

Physical Significance of the Planck Density

The Planck density is the Planck mass devided by the Planck volume, approximately 1093 g/cm3. Does this quantity have any known physical relevance? The Planck mass is believed to be the smallest ...
2
votes
1answer
60 views

Commutator of fermionic operators

The fermionic creation/annihilation operators are defined by the anti-commutation relations: $$ \{a_k^{\dagger},a_q^{\dagger}\} = 0 = \{a_k,a_q \} $$ $$ \{a_k^{\dagger},a_q\} = \delta_{kq} \, .$$ I ...
1
vote
0answers
30 views

Pion decay exercise in Griffiths books

I have questions about pion decay problem. In Griffith "Introduction to Elementary Particles" 1st edition, 1987, question number 10.10 : Analyze $\pi^-$ decay as a scattering process, using the ...
1
vote
2answers
49 views

How to verify/falsify the existence of localised edge states numerically?

I have to consider a Hamiltonian given in second quantized form in real space $$H = \sum c_k^\dagger h_{kl} c_l \, ,$$ describing fermions on a 2d hypercubic lattice. The concrete form of the matrix ...
0
votes
0answers
47 views

Computing the probability density of wavefunctions

Suppose I am given a Hamiltonian operator $\hat{H}$ that satisfies the time-independent Schrödinger equation $$\hat{H} \psi = E\psi$$ I can compute energy eigenvalues and their associated ...
-2
votes
0answers
46 views

Why Position & Momentum but NOT Position & Forces involved were considered in Uncertainity Principle?

Why Position and Momentum are considered in Uncertainity Principle? What I understood is that we can predict the future state of system if we know the position and momentum of all particles ...
0
votes
0answers
47 views

What does Bell's theorem rule out?

What exactly did Bell's theorem rule out? Did it rule out "locality", so we must give up and think of Copenhagen or maybe some realism theories (Bohmian for example)? ... That's how I understand ...
0
votes
2answers
64 views

Are matter waves (de Broglie) classified as transverse or longitudinal? [duplicate]

We know that waves are of two types: transverse and longitudinal, and we have studied about de Broglie waves as well, so which one of them is it? Or we have other means to classify them?
1
vote
0answers
19 views

Are there any in depth superfluid mechanic analyses of spacetime?

Has there been much work done that treats particles as vortexes in a fluid, or dark matter as bubbles in this fluid (bending space in the same way massive particles (vortexes) are observed to do, but ...
3
votes
0answers
41 views

MRI and precession

A lot of explanations of the quantum mechanics of MRI discuss the precession of a proton in an external magnetic field, for example here: http://www.physicscentral.com/explore/action/mri.cfm Doing ...
1
vote
1answer
36 views

The Sturm-Liouville equations, the Schrodinger equation and the wave equation

I heard in a online quantum mechanics lecture that Schrödinger equation is an instance of the Sturm-Liouville equation and that is the super position of its stationary states gives the most general ...
56
votes
6answers
10k views

Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?

I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance. Am I ...
5
votes
1answer
70 views

Has anyone published the procedure to generalize ladder operators for any potential in Schrodinger's equation?

I know that the ladder operator for the quantum harmonic oscillator \begin{align} H\psi_m = \left(\dfrac{p^2}{2m}+\dfrac{1}{2}m\omega^2x^2\right)\psi_m=E_m\psi_m \end{align} is \begin{align} A = ...
1
vote
2answers
34 views

Experimental verification of bound state transition times

I am trying to reconcile, what to me at least, are two slightly different answers to what I think is the same question. The first answer below to an earlier OP implies to me that there is a definite ...
1
vote
0answers
43 views

Schrodinger eqn with 'rescaled' Hamiltonian

If $U_t$ (time evolution operator) is the solution to the following Schrodinger equation for a time dependent finite dimentional quantum system: $\frac{d U_t}{dt} = -i H_t U_t$ can the solution to ...
0
votes
0answers
41 views

Why position and momenta are fluctuating quantities?

In a coordinate basis we have $$\langle \Psi \mid \Psi \rangle = \int \prod_{i=1}^N d^3q_i |\Psi(\textbf{q}_1,\dots,\textbf{q}_N)|^2=1$$ This means that for any quantum state $\mid \Psi ...
0
votes
2answers
71 views

Theoretically, is it necessary that if light passes through a glass slab, its intensity should decrease?

Is it necessary that for an E/M wave of given frequency which can pass through a medium of given refractive index, it should lose some of its intensity. Practically, this must be necessary because of ...
0
votes
0answers
30 views

Identity and indistinguishability in quantum and statistical mechanics [closed]

My question is on the use of the concept of indistinguishable particles (in quantum mechanics) in a very general context and in particular in statistical mechanics. I have made clear some of my ...
3
votes
1answer
37 views

Bell inequality with triplet state

Is it possible to prove Bell inequality starting from a state formed from triplet states, i.e. $\frac{1}{\sqrt{2}}(|\uparrow>_A|\uparrow>_B+|\downarrow>_A|\downarrow>_B)$? If not, why? ...
0
votes
2answers
57 views

Bohr/De Broglie simplfied model - joining orbitals

I understand that Quantum Mechanics has taken over and fully explains this but I'm struggling to understand in terms of the old model. Bohr's model as modified by de Broglie suggested that orbits ...
1
vote
3answers
67 views

Could all the electrons from the metal be ejected out during photoelectric effect?

During photoelectric effect when an electron absorbs a photon having energy greater than the threshold energy,it is ejected from the metal So when the metal continuously gets photons then could all ...
0
votes
1answer
49 views

If we hit an electron will it go to an excited state?

For example i have a block of silicon doped with phosphorous and i hit it hard with a hammer will the energy get transfered to the block and make the electrons excited?
0
votes
1answer
29 views

How does a photon drive out the electrons in a solar cell?

We know that solar cells work when a photon hits the n-type the photon's energy drives free the electrons in the n-type to generate a current. But we also know that when a photon hits the atoms it ...
2
votes
0answers
45 views

How to do time evolution of operators in the Heisenberg Picture while staying in the Heisenberg Picture

Consider the time evolution of an operator in the Heisenberg picture: $$\tag{1}i\hbar \frac{d}{d t} \hat{A}_{H}(t) = \left([ \hat{A}_S(t), \hat H_S (t)] + i\hbar \frac{d}{d t} \hat{A}_S(t) ...
0
votes
1answer
44 views

Two particle operator

Why is the two-particle (fermionic, cause for bosonic operators it is immediately clear that both representations are the same) Hamiltonian given by $$ H = \sum_{a,b,c,d} \langle ab|V|cd \rangle ...
2
votes
2answers
123 views

How did Planck derive his formula $E=hf$?

Some time ago I asked my quantum physics lecturer the question: How did Planck derive his formula, the Planck–Einstein relation $$E=hf$$ with constant of proportionality $h$, the Planck ...
6
votes
3answers
620 views

Does it mean anything if the commutator of an operator with the Hamiltonian is equal to the Hamiltonian?

Question says it all, really. I have $[\hat{H},\hat{O}]=-2i\hbar\hat{H}$. Does this mean that the operator $\hat{O}$ (an observable) is special in some way?
0
votes
0answers
37 views

What is the difference between Fermi golden rule and Wigner-Weisskopf theory?

What is the difference between Fermi golden rule and Wigner-Weisskopf theory? They both deal with the spontaneous emission process. So what is the difference? As far as I know, the fermi golden rule ...
0
votes
0answers
24 views

Identity operator in terms of the energy eigenstates in case of continuous spectrum

Let us confine ourselves to the 1d case. If we define the momentum eigenvector $|k\rangle $ as $$ \langle x |k\rangle = \frac{1}{\sqrt{2\pi}} e^{i k x} ,$$ we have the identity operator decomposed ...
-1
votes
1answer
68 views

Can we disconnect an object from the pull of gravity using some material? [duplicate]

I have once come across a material/ substance/ compound, or something, that cuts off objects from Earth's gravitational pull. In other words, it would keep the object suspended in the air and will ...
0
votes
0answers
71 views

Macroscopic polarization operator (Berry's phase?)

I am faced with the problem of extracting the velocity from a density matrix which has a periodic nature with infinite spatial extent. This density matrix has time harmonic terms which hold the ...
0
votes
0answers
19 views

Tunnel diode/quantum tunneling

How does a tunnel diode work?/How does a tunnel diode use quantum tunneling, and how does quantum tunneling make the diode faster?
1
vote
1answer
34 views

Are measurement results only orthogonal?

Are all measurement operators on a quantum mechanical system defined by a Hilbert space, such that all possible post-measurement states are orthogonal? For example measuring a qubit in some ...
2
votes
0answers
32 views

Why is the water diamagnetic?

I checked using my permanent magnet that water is diamagnetic. But why is it like that? Does this have any important consequence for life?