Theoretical Physics on the Personal Computer

Schmid, Erich W.; Spitz, Gerhard; Lösch, Wolfgang

doi:10.1007/978-3-642-75471-5

Cited by 7 publications

(3 citation statements)

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“…The parameters L, L ′ , M , and N , corresponding to different parts of the Hamiltonian, are given by L =4 + 30c 1 + 48c 2 + 72c Aside from units (most treatments use so-called chemistry units) these all agree with results in the literature. 3,20 Use of the optimally determined parameters, c 1 ≈ 0.0803 and c 2 ≈ 0.0099, and k ≈ 0.908 determines the energy via Eq. (B1).…”

Section: Matrix Equation For Imax =mentioning

confidence: 99%

The spectral decomposition of the helium atom two-electron configuration in terms of hydrogenic orbitals

Hutchinson¹,

Baker²,

Marsiglio³

2012

Eur. J. Phys.

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The two electron configuration in the Helium atom is known to very high precision. Yet, we tend to refer to this configuration as a 1s ↑ 1s ↓ singlet, where the designations refer to Hydrogen orbitals. The high precision calculations utilize basis sets that are suited for high accuracy and ease of calculation, but do not really aid in our understanding of the electron configuration in terms of product states of Hydrogen orbitals. Since undergraduate students are generally taught to think of Helium, and indeed, the rest of the periodic table, in terms of Hydrogenic orbitals, we present in this paper a detailed spectral decomposition of the two electron ground state for Helium in terms of these basis states. The 1s ↑ 1s ↓ singlet contributes less than 93% to the ground state configuration, with other contributions coming from both bound and continuum Hydrogenic states.

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Section: Matrix Equation For Imax =mentioning

confidence: 99%

The spectral decomposition of the helium atom two-electron configuration in terms of hydrogenic orbitals

Hutchinson¹,

Baker²,

Marsiglio³

2012

Eur. J. Phys.

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“…Berdasarkan dua persamaan getaran selaras tergandeng pada persamaan (1) dan ( 2) dan mengacu pada penelitian sebelumnya (Schmid dkk, 1990dan Arafah, 2001 serta Sulaiman ( 2008), maka dapat diuraikan sebagai berikut:…”

Section: Gambar 1 Kasus Getaran Tergandengunclassified

Visualisasi Fenomena Harmonis Dan Chaos Pada Getaran Tergandeng Berbasis Komputasi Numerik Runge Kutta

Trifina,

Warsito,

Lapono

et al. 2023

fisa

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Research has been carried out on the visualization of harmonic and chaos phenomenont on coupled vibration physcal case using the Runge Kutta numerical computation method with the aim of applying the first to fourth order Runge Kutta computation method to obtain a second order differential equation solution on coupled vibration system, calculating the displacement value of objects using computation method Runge Kutta order first to fourth, obtained a graph of the displacement of objects againts time in case of coupled vibration for harmonic and chaos states at certain step width values and compare the convergence of the Runge Kutta method from first to fourth order with the special analytical method. The solution of coupled vibration equation which is classified as a second order differential equation was quite difficulted to solve analytically, so the Runge Kutta computation method was used to solve it as an alternative solution. The results of the research showed that the harmonic state of the system was obtained when the displacement graph showed the motion of each pendulum which was constant with the pendulum displacement position with respect to time in the form of a sinusoidal graph at a value of C1 = 40 N/m, C2 = 30 N/m, C = 10 N/m, C = 0 N/m and the chaotic state was represented by a graph of the displacement of the pendulum with respect to time with an irregular pattern. In this case, it was found that the fourth order Runge Kutta method converged faster than the first to third order Runge Kutta method with the best results obtained at a step width value of 0,001. The fourth order Runge Kutta method also has a smaller approximation average error value from first to third order Runge Kutta method was on the fourth order Runge Kutta method and the avarage error values are , and on the Runge Kutta method of first to third order.

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“…The resulting phase shift is determined by gluing the numerical solution with asymptotic one at the endpoint of the grid [34]:…”

Section: B Dark Matter Self-interactionsmentioning

confidence: 99%

Self-interacting dark matter from late decays and the $H_0$ tension

Hryczuk,

Jodłowski

2020

Preprint

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We study a dark matter production mechanism based on decays of a messenger WIMP-like state into a pair of dark matter particles that are self-interacting via exchange of a light mediator. Its distinctive thermal history allows the mediator to be stable and therefore avoid strong limits from the cosmic microwave background and indirect detection. A natural by-product of this mechanism is a possibility of a late time, i.e., after recombination, transition to subdominant dark radiation component through three-body and one-loop decays to states containing the light mediator. We examine to what extent such a process can help to alleviate the H0 tension. Additionally, the mechanism can provide a natural way of constructing dark matter models with ultra-strong self-interactions that may positively affect the supermassive black hole formation rate. We provide a simple realization of the mechanism in a Higgs portal dark matter model and find a significant region of the parameter space that leads to a mild relaxation of the Hubble tension while simultaneously having the potential of addressing small-scale structure problems of ΛCDM.

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Theoretical Physics on the Personal Computer

Cited by 7 publications

References 0 publications

The spectral decomposition of the helium atom two-electron configuration in terms of hydrogenic orbitals

The spectral decomposition of the helium atom two-electron configuration in terms of hydrogenic orbitals

Visualisasi Fenomena Harmonis Dan Chaos Pada Getaran Tergandeng Berbasis Komputasi Numerik Runge Kutta

Self-interacting dark matter from late decays and the $H_0$ tension

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