# What is Quantum mechaincs: Definition and 109 Discussions

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1. ### I I want to expand a Gaussian wavepacket in terms of sines

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...
2. ### A Anti-commutation relation for quantized fields

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...
3. ### B Questions about the Universe: Positive & negative fields and effects

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...
4. ### A What’s the meaning of decay rate in optical Bloch equations?

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
5. ### A Multiparticle Relativistic Quantum Mechanics in an external potential

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...
6. ### I Superconductors and moving/accelerating charges

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...
7. ### I Understanding the diagonal elements of the transition dipole moment

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...
8. ### Verifying that the uncertainty is 0 for a QM state

By definition , ##\ket{+x} = \alpha \ket{+z} + \beta \ket{-z}.## Therefore we proceed , \begin{align*} \langle S_{x} \rangle &= \lvert \alpha \rvert^{2} \left(\frac{\hbar}{2}\right) + \lvert \beta\rvert^{2} \left(-\frac{\hbar}{2}\right) = (\alpha^{2} - \beta^{2})\left(\frac{\hbar}{2}\right).\\...
9. ### Quantum Dirac notation based quantum books?

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...

27. ### A Using feedback in quantum measurements

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...
28. ### Flux-flux correlation function under Feynman's path integral

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...
29. ### B Quantum mechanic has something to do with electromagnetism?

Hi does the quantum mechanic play a role in the intrinsic nature of electromagnetic fields and its propagation? massi
30. ### A A surprise result using Helmann-type potential

\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...
31. ### Near-resonant excitation of a two-level system

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...
32. ### I Singlet State: Symmetry vs Antisymmetry

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...
33. ### Understanding Hermitian Operators: Exploring Their Properties and Applications

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...
34. ### Given wavenumber find spring constant harmonic oscillator

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 =...
35. ### B Quantum field theory VS Quantum mechanics

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?
36. ### B Position of a particle immediately after a measurement

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?
37. ### Bohr frequency of an expectation value?

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...
38. ### B Double Slit Experiment: Feynman's Lectures

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...
39. ### Applying the grand canonical ensemble to a magnetic system

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...
40. ### I The barrier length in quantum tunneling

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...
41. ### Phase transition at high energies?

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")
42. ### Exploring the Wave-Particle Duality of Electrons in CRT Monitors

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?
43. ### What is the explanation for the differential form of Planck's law?

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...
44. ### Matrix elements of non-normalizable states

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}## ##...
45. ### What is the energy of a hydrogen atom in a mixed state?

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.
46. ### Quantum Mechanics Simulations - Project

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...
47. ### Rotation transformation by poisson brackets

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.
48. ### Does the Higgs field truly exist if it cannot be directly measured?

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...
49. ### Deriving Hamiltonian in Landau Gauge Using Symmetric Gauge Transformation

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...
50. ### Dimensionless Radial Equation Hydrogen Atom

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}##...