Partial differential equations | Quantum models

Particle in a spherically symmetric potential

In the quantum mechanics description of a particle in spherical coordinates, a spherically symmetric potential, is a potential that depends only on the distance between the particle and a defined centre point. In particular, if the particle in question is an electron and the potential is derived from Coulomb's law, then the problem can be used to describe a hydrogen-like (one-electron) atom (or ion). In the general case, the dynamics of a particle in a spherically symmetric potential are governed by a Hamiltonian of the following form: Where is the mass of the particle, is the momentum operator, and the potential depends only on , the modulus of the radius vector r. The quantum mechanical wavefunctions and energies (eigenvalues) are found by solving the Schrödinger equation with this Hamiltonian. Due to the spherical symmetry of the system, it is natural to use spherical coordinates , and . When this is done, the time-independent Schrödinger equation for the system is separable, allowing the angular problems to be dealt with easily, and leaving an ordinary differential equation in to determine the energies for the particular potential under discussion. (Wikipedia).

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Particles with spin interacting with a potential with pentagonal symmetry

This video shows 915 particles interacting with a Lennard-Jones potential with a directional dependence having the symmetry of a regular pentagon, similar to the video https://youtu.be/zz6OEZ0TBxk . However, here every particle has its own orientation, or "spin", defining the interaction's

From playlist Molecular dynamics

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Charged particle in a magnetic field

Helicoidal motion of a charged particle in a uniform magnetic field. For other animations like this one, please visit http://web.ncf.ca/ch865

From playlist Magnetic Fields

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Freezing and melting of particles with anisotropic Lennard-Jones interaction

In this simulation, particles interact with an anisotropic version of the Lennard-Jones potential, which favors the horizontal, vertical, and diagonal directions. Any two particles, when far away from all other particles, would form a stable configuration when they are situated on vertices

From playlist Molecular dynamics

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An attempt at growing a quasicrystal

Like the simulation https://youtu.be/YjerTwsRUp0 this one shows the motion of particles coupled to a thermostat, and interacting with an anisotropic Lennard-Jones type potential. Only this time, the potential has a pentagonal symmetry instead of a square symmetry. Two isolated particles ha

From playlist Molecular dynamics

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Physics 38 Electrical Potential (12 of 22) Potential In-, On, & Outside a Spherical Conductor

Visit http://ilectureonline.com for more math and science lectures! In this video I will find the potential inside, at the surface, and outside of a spherical conductor.

From playlist PHYSICS 38 ELECTRICAL POTENTIAL

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Physics - Mechanics: Ch. 18.1: Gravity with Mass Distribition (15 of 17) Grav. Potential In

Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the gravitational potential IN a spherical shell. Next video in this series can be found at: https://youtu.be/0LF1wuRsOrQ

From playlist PHYSICS 18.1 GRAVITY WITH MASS DISTRIBUTION

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Self-assembly of Linear polymer chains using spherically symmetric potentials by Apratim Chatterji

Indian Statistical Physics Community Meeting 2018 DATE:16 February 2018 to 18 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore This is an annual discussion meeting of the Indian statistical physics community which is attended by scientists, postdoctoral fellows, and graduate s

From playlist Indian Statistical Physics Community Meeting 2018

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Molecular dynamics with pentagonal symmetry, a representation with atomic bonds

Like the simulation https://youtu.be/absx0JHkUn8 this video shows the motion of particles coupled to a thermostat, and interacting with an anisotropic Lennard-Jones type potential with pentagonal symmetry. Here the lattice is visualized by drawing line segments between particles that are c

From playlist Molecular dynamics

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A molecular chessboard: particles with spin interacting with a square-symmetric potential

This simulation shows 1566 particles interacting with a potential that depends on their orientation, or "spin". The spins evolve through a coupling torque depending in the difference of their angles, as in the XY model for ferromagnets or in the Kuramoto model for synchronization, which te

From playlist Molecular dynamics

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[Lesson 9] QED Prerequisites - Mind Map of Angular Momentum Part I

This is the start of a high level review of the Quantum Theory of Angular Momentum. It is intended to point you into directions for deeper review. This material will lead us to our detailed review of non-relativistic scattering theory. Please consider supporting this channel on Patreon: h

From playlist QED- Prerequisite Topics

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L22.3 Diagrammatic representation of the Born series. Scattering amplitude for spherically symm...

MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L22.3 Diagrammatic representation of the Born series. Scattering amplitud

From playlist MIT 8.06 Quantum Physics III, Spring 2018

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A quantum particle in a constant magnetic field

This is a first attempt at simulating a quantum particle in a magnetic field. The particle moves in a plane, and the magnetic field is constant, and perpendicular to the plane. The vector potential used in Schrödinger's equation is proportional to the vector (y, -x, 0). I hope to be able t

From playlist Schrödinger's equation

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Mean field approximations to n-body projection Hamiltonians in FQHE by Sreejith G J

Indian Statistical Physics Community Meeting 2018 DATE:16 February 2018 to 18 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore This is an annual discussion meeting of the Indian statistical physics community which is attended by scientists, postdoctoral fellows, and graduate s

From playlist Indian Statistical Physics Community Meeting 2018

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Quantum Mechanics {Texas A&M: Intro to Materials}

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From playlist TAMU: Introduction to Materials Science & Engineering | CosmoLearning.org

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Thomas Baumgarte (1) - Numerical relativity: Mathematical formulation

PROGRAM: NUMERICAL RELATIVITY DATES: Monday 10 Jun, 2013 - Friday 05 Jul, 2013 VENUE: ICTS-TIFR, IISc Campus, Bangalore DETAL Numerical relativity deals with solving Einstein's field equations using supercomputers. Numerical relativity is an essential tool for the accurate modeling of a wi

From playlist Numerical Relativity

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On the anomalous thermomechanics of dry active matter (Remote talk) by Julien Tailleur

PROGRAM : FLUCTUATIONS IN NONEQUILIBRIUM SYSTEMS: THEORY AND APPLICATIONS ORGANIZERS : Urna Basu and Anupam Kundu DATE : 09 March 2020 to 19 March 2020 VENUE : Madhava Lecture Hall, ICTS, Bangalore THIS PROGRAM HAS BEEN MODIFIED ONLY FOR LOCAL (BANGALORE) PARTICIPANTS DUE TO COVID-19 RI

From playlist Fluctuations in Nonequilibrium Systems: Theory and Applications

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Pressure in non-equilibrium (active) systems by Yariv Kafri

PROGRAM URL : http://www.icts.res.in/program/NESP2015 DATES : Monday 26 Oct, 2015 - Friday 20 Nov, 2015 VENUE : Ramanujan Lecture Hall, ICTS Bangalore DESCRIPTION : This program will be organized as an advanced discussion workshop on some topical issues in nonequilibrium statstical phys

From playlist Non-equilibrium statistical physics

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Dmitriy Bilyk: On the interplay between uniform distribution,discrepancy, and energy

VIRTUAL LECTURE Recording during the meeting "Discrepancy Theory and Applications". Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywo

From playlist Analysis and its Applications

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Physics - E&M: Maxwell's Equations (22 of 30) Differential Form of Ampere's Law: 3

Visit http://ilectureonline.com for more math and science lectures! In this video I will find the curl of the B-field of a cylindrical conductor.

From playlist PHYSICS 46 MAXWELL'S EQUATIONS

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Black hole perturbation theory (lecture 4) by Emanuele Berti

DATES Monday 25 Jul, 2016 - Friday 05 Aug, 2016 VENUE Madhava Lecture Hall, ICTS Bangalore APPLY Over the last three years ICTS has been organizing successful summer/winter schools on various topics of gravitational-wave (GW) physics and astronomy. Each school from this series aimed at foc

From playlist Summer School on Gravitational-Wave Astronomy

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