From this paper, I am trying to compute the coefficients in the expansion of the Gaussian wavepacket
$$\phi(x) = \frac{1}{(2\pi\sigma^2)^{\frac{1}{4}}}\exp \Big(-\frac{(x-x_{0})^{2}}{4\sigma^{2}} + ik_{0}(x-x_{0})\Big) $$ where $$\sigma << 1$$and $$k_{0} >> \frac{1}{\sigma}$$
in terms of the...
Could somebody elaborate following statement from wikipedia in detail on interplay between the "choice" of anti- or commutation relation for quantized fields and the the associated statistics which the field satisfies before get quantized:
Very roughly the story with second quantization is one...
So I saw an article about the universe and lets say the article saied:
the essence of the universe, which is impossible, as it has been proven that universal constants such as the gravitational constant and the speed of light indicate the existence of unified physical laws that govern the entire...
i have some questions about decay rate.
1：why do we need decay rate in these equations?
2：is it a constant for a specific medium?
3：it can be changed with respect to some conditions like temprature or pressure?
4：how can i know the decay rate of some energy levels in 85Rubidium
It is often argued that Dirac Equation is not valid as relativistic quantum mechanics requires the creation of antiparticles. But, there are also some arguments that suggest otherwise. For example, I saw Arnold Neumaier's website on this that there are multiparticle relativistic quantum...
How do one get the electrons to move inside a superconductor? Since I have understood superconductors repel magnetic fields due to the Meissner effect, or is that when the charges already are moving within the superconductor? If so how did we get them o move from the beginning?
Can you make...
Hey guys, I just numerically calculated the matrix elements for a superconducting qubit and I'm having some trouble to interpret the result.
I will include a plot of the matrix I got below:
I basically have "large" non zero elements on the main diagonal of this matrix. In previous courses I...
hi
i am recently following the nptel course in quantum mechanics (The Course ) and it seems like a really good course , but i can't find
the book that it based on .
my question is : had anyone saw that course before to suggest a QM book related to it ?
- she began by an introduction to vector...
Part a: Using the above equation. I got
$$\psi(x) = \int_{-\infty}^{\infty} \frac{Ne^{ikx}}{k^2 + \alpha^2}dk $$
So basically I needed to solve above integral to get the wave function. To solve it, I used Jordan's Lemma & Cauchy Residue Theorem.
And obtained $$\psi(x) = \frac {N \pi...
For the given problem, I know that the quantized energy for the particles in a 1D box is given by -
E(n) = n^2 h^2/ (8mL^2)
Here m = mass of electron
L = Length of the box = a
Now, since there are 8 electrons, but only 2 can occupy one energy level,
so I used n^2 = (1)^2 + (2)^2 = 1 + 4 = 5...
Summary:: My skills are very very basic and I'm more a networking major but i had to take a quantum mechanics class, i have trouble with this xcercise from textbook quantum mechanics a general introduction
[Mentor Note -- Thread moved from the Technical forums so no Homework Template is shown]...
Hi,
usually, when we talk about quantum quench dynamics we assume situation when Hamiltonian of a system has a sudden change from ##H_0## to ##H_1##. System was initially in the ground state (or more generally - eigenstate) of ##H_0##. The interesting dynamics appears when the commutator...
Let's say I have a system whose time evolution looks something like this:
This equation tells me that if I measure energy on it, I will get either energy reading ## E_0 ## or energy reading ## E_1 ## , when I do that, the system will "collapse" into one of the energy eigenstates, ## \psi_0 ##...
Homework Statement
Given the above lambda system, is it wrong to say that the density matrix is of the form ## \rho = c_1|1> + c_2|2> + c_3|3> ## ? Hence when written in matrix form (basis of ##|i>##), ## \rho ## is a diagonal matrix who's elements are the ##c_i##s?
I’m currently self-studying from Feynman & Hibbs Quantum Mechanics and Path Integrals, but having trouble with a statement in the chapter on time-dependent perturbations.
Background: They define
$$V_{mn}(t_c) = \int_{-\infty}^\infty \phi_m^*(x_c)V(x_c,t_c)\phi_n(x_c)\,dx_c,$$
where V(x,t) is...
Homework Statement
The Ca spectrum below, recorded using a Fourier Transform Spectrometer (FTS), shows the resolved ##3d4s ^3D - 3d4p ^3D## multiplet. The wavenumbers and their relative intensities are given in the table. Identify all the lines and determine the fine structure constants in the...
I am trying to read about and understand string theory. But in trying to understand how it reconciles with the world of quantum field theory and quantum mechanics, I am getting a little confused. How does the string move through and propagate through the quantum field?
Does string theory...
Homework Statement
A particle with mass m is moving on the x-axis and is described by
## \psi_b = \sqrt{b} \cdot e^{-b |x|}##
Find the probability distribution for the particles momentum
Homework Equations
## \Phi (p)= \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^\infty \Psi(x,0) \cdot e^{-ipx} dx##...
Homework Statement
specific lagrangian is defined.
Have to get a equation of motion
Homework Equations
[/B]
Lagrangian is defined as
The Attempt at a Solution
[/B]
eq of motion that i drive like
i guess term of f(x) have to vanish or form a shape of curl.
but it didn't be clear...
I would be in college in 2019 (currently I'm in standard 11). I'm greatly interested in Quantum mechanics, QFT, QCD and Quantum Geometerodynamics. Of these, I want to do an internship on the first, because I don't think I'll be able to touch the others till the 2nd year in college.
I'm living...
Homework Statement
The Hamiltonian of a spin 1/2 particle is given by:
$$H=g\overrightarrow { S }\cdot \overrightarrow { B } $$
where ##\overrightarrow { S }=\hbar \overrightarrow{\sigma }/2## is the spin operator and ##\overrightarrow { B }## is an external magnetic field.
1. Determine...
How can volumes and hypervolumes be related to Einstein's theory of special relativity and to quantum mechanics? Also, can volumes and hypervolumes of objects be used for modeling how different scenarios can change over time? Oh yeah, and hi my name is Sasha Jaffarove!
Folks - I'm asking a lot of questions lately (hopefully useful not just for me).
By chance, reading about quantum states, I referenced Wikipedia (dubious I know), and came across the following phrase (with a citation, that I will check): "Even in quantum theory, however, for every observable...
An electron can tunnel between potential wells. Its state can be written as:
$$
|\psi\rangle=\sum^\infty_{-\infty}a_n|n\rangle
$$
Where $|n \rangle$ is the state at which it is in the $n$th potential well, n increases from left to right.
$$...
If we consider an efficient measurement performed on a system in a pure state. How would we use feedback (by applying to the system a unitary operator that depends upon the measurement result), to prepare the system in the same final state for every outcome of the measurement (this can be done...
This is a chemically inspired problem, but the path is fully quantum mechanics and a bunch of integrals.
How does one calculate fully quantum mechanical rate ($\kappa$) in the golden-rule approximation for two linear potential energy surfaces?
Attempt:
Miller (83) proposes...
\begin{align}
V(r,a)=\frac{e^2}{r}-\frac{e^2}{r}exp(\frac{-r}{a})
\end{align}
The above equation is called Helmann type potential which is a combination of Yukawa and coulomb potential. It is used to solve many problems in physics, for example
https://arxiv.org/pdf/1307.2983.pdf
But I...
Homework Statement
Hello, I have the following task:
[/B]
Homework Equations
In the task[/B]
The Attempt at a Solution
I looked at this task with the notes from the class, but I can't really see through. It seems that the first step is the transformation into the single decoupled...
Hello! I am a bit confused about the relation between the singlet configuration and symmetry of the system. So in the spin case, for 2, 1/2 particles, the singlet configuration is antisymmetric. But I read that the quarks are always in a singlet configuration, which means that they are symmetric...
Basically I've seen some expressions involving Hermitian Operators that I can't seem to justify, that others on the internet throw around like axiomatic starting points.
(AB+BA)+ = (AB)++(BA)+? Why does this work?
Assuming A&B are hermitian, I get why we can assume A+B is hermitian, but does...
Homework Statement
The separation between energies of an oxygen molecule is 2061 cm-1 (wavenumber). Treating the molecule as a simple harmonic oscillator whose fundamental frequency is related to its spring constant and reduced mass, calculate the spring constant for an O2 molecule.
meff =...
Hello I am little bit confused about one topic on theoretical Physics and that is If we want to describe our Quantum world (example atoms in metal) then should I use Quantum field theory or Quantum mechanics?
Say a particle was measured to be at a point C. Immediately after this, if i make another measurement, its given in griffith's book that the particle will still be found at C. Isn't this only possible if the particle was at rest?
Homework Statement
Consider a two-state system with a Hamiltonian defined as
\begin{bmatrix}
E_1 &0 \\
0 & E_2
\end{bmatrix}
Another observable, ##A##, is given (in the same basis) by
\begin{bmatrix}
0 &a \\
a & 0
\end{bmatrix}
where ##a\in\mathbb{R}^+##.
The initial state of the system...
In the third book of Feymann's Lectures on Physics(section 1-8) he describes how "the Uncertainty Principle protects Quantum Mechanics." The experimental situation is a modified double slit experiment where the two slits are put on rollers in an attempt to detect which slit an electron passes...
Homework Statement
Consider a system with N sites and N particles with magnetic moment m. Each site can be in one of three states: empty with energy 0, occupied by one particle with energy 0 (in the absent of magnetic field) or occupied by two particles with anti parallel moments and energy ε...
Hi,
In transmission coefficient T= exp(-2sqrt(2m(U-E)/hbar^2)L), L, as I interpret it, is the distance of the potential barrier. I am wondering if I have N particles all with kinetic energy E, approaching the barrier, can I integrate the transmission coefficient over a distance from infinity to...
Hi,I'm new here,
and created my account solely for following question:
Does the incompatibility between QM and Relativity indicate a phase transition at high energies?
(as in: indicate more than a "could be")
How do CRTs work well and electrons can be sent to exact location on screen in CRT monitors if electrons can behave like wave?
Is there something in old TVs (for example measurement device) along the road that electron travels to avoid behave like wave?
Hello!
I have a little trouble with understanding Planck's law of radiation, and wondered if you could help me with it. :)
The equation is:
## \frac{dI}{d\lambda} = \frac{2\pi hc^2}{\lambda^5(e^{hc/\lambda kT}-1)} ## (1)
where T is the temperature, k Boltzmann's constant, h Planck's constant...
Although strictly quantum mechanics is defined in ##L_2## (square integrable function space)， non normalizable states exists in literature.
In this case, textbooks adopt an alternative normalization condition. for example, for ##\psi_p(x)=\frac{1}{2\pi\hbar}e^{ipx/\hbar}##
##...
Suppose a single hydrogen atom is in mixed state.
Ψ=(1/√2) Ψ_100+(1/√2) Ψ_200
Then energy will be E=(1/2)*13.6+(1/2)*(3.4)=8.5 eV.
But there is no spectral line at 8.5 eV.
Hello.
I am not too sure if this thread is the right place to post this in. But anyway.
I have to make a project for my final year, and I have chosen to make a quantum mechanics based project. I am thinking of doing some quantum mechanics based simulations, give a little bit of history of...
Homework Statement
Can anybody suggest hints on how to show that x'=xcosΘ-ysinΘ, y'=xsinΘ+ycosΘ by using the infinite string of poisson brackets?
Homework Equations
ω→ω+a{ω,p}+a^2/2!{{ω,p},p}+...
The Attempt at a Solution
Sorry, I just can’t think of any way, substituting doesn’t work.
In QFT particles are described by fields, but AFAIK these fields are mathematical since we don't measure values of fields at a particular spacetime. So what does it mean to say a higgs field exist!
I mean it is one thing to say Higgs particle exists (in LHC), but I have not seen anybody measure...
Homework Statement
Define n=(x + iy)/(2)½L and ñ=(x - iy)/(2)½L.
Also, ∂n = L(∂x - i ∂y)/(2)½ and ∂ñ = L(∂x + i ∂y)/(2)½.
with ∂n=∂/∂n, ∂x=∂/∂x, ∂y=∂/∂y, and L being the magnetic length.
a=(1/2)ñ+∂n and a†=(1/2)n -∂ñ
a and a† are the lowering and raising operators of quantum mechanics.
Show...
Homework Statement
Show that in terms of the dimensionless variable ##\xi## the radial equation becomes ##\frac{\mathrm{d}^{2} u}{\mathrm{d} \xi^{2}}=(\frac{l(l+1)}{\xi^{2}}-\frac{2}{\xi}-K)u##
Homework Equations
##u(r)\equiv rR(r)##
##\xi \equiv \sqrt{2\mu U_{0}}\frac{r}{\hbar}##...