In quantum mechanics, the variational method is one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states. This allows calculating approximate wavefunctions such as molecular orbitals. The basis for this method is the variational principle. The method consists of choosing a "trial wavefunction" depending on one or more parameters, and finding the values of these parameters for which the expectation value of the energy is the lowest possible. The wavefunction obtained by fixing the parameters to such values is then an approximation to the ground state wavefunction, and the expectation value of the energy in that state is an upper bound to the ground state energy. The Hartree–Fock method, Density matrix renormalization group, and Ritz method apply the variational method. (Wikipedia).
Variational Principle Introduction
In this video, I introduce the variational principle in quantum mechanics, how it is derived, and why you might want to use it. Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos. This
From playlist Quantum Mechanics
How to Get Classical Physics from Quantum Mechanics
We tend to think of Classical Physics as straightforward and intuitive and Quantum Mechanics as difficult and conceptually challenging. However, this is not always the case! In classical mechanics, a standard technique for finding the evolution equations for a system is the method of least
From playlist Quantum Mechanics
Carlos Bravo-Prieto - Variational quantum architectures for linear algebra applications
Recorded 27 January 2022. Carlos Bravo-Prieto of the University of Barcelona presents "Variational quantum architectures for linear algebra applications" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Current quantum computers typically have a few tens of qubits and are pro
From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022
Variation of Parameters for Systems of Differential Equations
This is the second part of the variation of parameters-extravaganza! In this video, I show you how to use the same method in the last video to solve inhomogeneous systems of differential equations. Witness how linear algebra makes this method so elegant!
From playlist Differential equations
Time-Independent Schrödinger Equation | Quantum Mechanics
In this video, we will talk about the time-independent Schrödinger equation in quantum mechanics. If we start with the time-dependent Schrödinger equation, we can get to the time-independent one by performing a separation of variables on the wave function, where we claim that the time depe
From playlist Quantum Mechanics, Quantum Field Theory
Variational Methods | Quantum Mechanics
In this video, we will discuss variational methods, in particular the Ritz method for approaching the ground state energy of a system. If we look at a quantum mechanical system with Hamiltonian H, we always want to know: what's the ground state energy? Because that's the energy that the
From playlist Quantum Mechanics, Quantum Field Theory
Quantum Theory - Full Documentary HD
Check: https://youtu.be/Hs_chZSNL9I The World of Quantum - Full Documentary HD http://www.advexon.com For more Scientific DOCUMENTARIES. Subscribe for more Videos... Quantum mechanics (QM -- also known as quantum physics, or quantum theory) is a branch of physics which deals with physica
From playlist TV Appearances
Variation of Constants / Parameters
Download the free PDF http://tinyurl.com/EngMathYT A basic illustration of how to apply the variation of constants / parameters method to solve second order differential equations.
From playlist Differential equations
David Ceperley - Introduction to Classical and Quantum Monte Carlo methods for Many-Body systems
Recorded 09 March 2022. David Ceperley of the University of Illinois at Urbana-Champaign presents "Introduction to Classical and Quantum Monte Carlo methods for Many-Body systems" at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Abstract: Metropolis (Markov
From playlist Tutorials: Advancing Quantum Mechanics with Mathematics and Statistics - March 8-11, 2022
Free ebook http://tinyurl.com/EngMathYT I show how to solve differential equations by applying the method of variation of parameters for those wanting to review their understanding.
From playlist Differential equations
Kieron Burke - Elements of electronic structure calculations: HF and DFT - IPAM at UCLA
Recorded 08 March 2022. Kieron Burke of the University of California, Irvine, presents "Elements of electronic structure calculations: HF and DFT" at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Abstract: I will introduce basic concepts and methodology of m
From playlist Tutorials: Advancing Quantum Mechanics with Mathematics and Statistics - March 8-11, 2022
David Mazziotti - Contracted Quantum Eigensolver for the Quantum Simulation of Many-electron Systems
Recorded 05 May 2022. David Mazziotti of the University of Chicago, Chemistry, presents "Contracted Quantum Eigensolver for the Quantum Simulation of Many-electron Systems" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: We will introduce a novel
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
Han Pu: "Solving Quantum Many-Body Problems with Deep Neural Networks"
Machine Learning for Physics and the Physics of Learning 2019 Workshop I: From Passive to Active: Generative and Reinforcement Learning with Physics "Solving Quantum Many-Body Problems with Deep Neural Networks" Han Pu - Rice University Abstract: Inspired by their great success in variou
From playlist Machine Learning for Physics and the Physics of Learning 2019
Alexandre Tkatchenko - Many-body perturbation theory and wavefunction methods: A Physics perspective
Recorded 08 March 2022. Alexandre Tkatchenko of the University of Luxembourg presents "Many-body perturbation theory and wavefunction methods: A Physics perspective" at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Learn more online at: http://www.ipam.ucla.
From playlist Tutorials: Advancing Quantum Mechanics with Mathematics and Statistics - March 8-11, 2022
Enno Lenzmann Interpolations inequalities and applications to non linear PDE 4)
Enno Lenzmann (Basel, Switzerland) The course was given at the Institut Henri Poincaré (Paris) in June 2013, within a thematic trimester on "variational and spectral methods in quantum mechanics". The aim of the course was to discuss interpolation inequalities and their optimizers, as
From playlist T2-2013 : Variational and Spectral methods in quantum mechanics.
Zheng-Cheng Gu: "Emergent gapless quantum spin liquid from deconfined quantum critical point"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop II: Tensor Network States and Applications "The emergence of gapless quantum spin liquid near deconfined quantum critical point" Zheng-Cheng Gu - The Chinese University of Hong Kong Abstract: Deconfi
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021