Hydrogen Atom | Solving the Schrodinger Equation (Energy and Wavefunctions) скачать в хорошем качестве

Hydrogen Atom | Solving the Schrodinger Equation (Energy and Wavefunctions)

In this video, we start by reviewing how angular and radial differential equations look like and what effective potential in radial equation is and then try to solve the radial equation for the case of hydrogen atom. We see hydrogen atom as a system of two bodies, proton and electron, and assume that the nucleus (proton) is motionless and consider its influence on the electron as a coulomb's potential. By solving this equation we find a recursion formula by which we can find the energy values and also eigenfunctions of the Hamiltonian of this system. The wavefunctions can either be calculated by this recursion formula or associate Laguerre polynomials. We derive the energy values and also their wavefunctions for the ground state of the hydrogen atom and also the first excited state. If you don't know how to find the radial and angular part of the Schrodinger equation in three dimensions, I suggest that you watch these videos: How to solve the Schrodinger equation in three dimensions using separation of variables:    • Solving the Schrodinger Equation in Three ...   Solving the angular part and spherical harmonics (quantum numbers m and l):    • Solving the Schrodinger Equation in 3D | A...   Solving the radial equation and effective potential:    • Solving the Schrodinger Equation in 3D | I...   Bra-Ket notation:    • Dirac Notation (Bra-Ket) | Understanding t...   I hope you like this video. 00:00 Radial and angular equations (review) 02:14 Hydrogen atom 11:22 The ground state of hydrogen atom 15:53 The first excited state of hydrogen atom 19:26 Associated Laguerre polynomials