Particle in a 2-D box wavefunction derivation скачать в хорошем качестве

Particle in a 2-D box wavefunction derivation

00:08 Sketch of 2-D box 01:16 Generalized Schrödinger Equation 02:13 Schrödinger Equation in two Cartesian dimensions 03:07 Method of Separation of Variables 05:05 Calculation of second partial derivatives of trial wavefunction 07:18 Substitution of trial wavefunction of calculated second partial derivatives into Schrödinger Equation 08:53 Divide each side by X(x)Y(y) 11:02 Use fact that right hand side is constant (so independent of x) 11:55 Use fact that right hand side is constant (so independent of y) 12:55 Multiply each side by Y(y) 13:42 Solve first order Schrödinger Equation in y 15:33 Multiply each side by X(x) 15:59 Solve first order Schrödinger Equation in x 17:49 Substitute eigenfunctions into trial wavefunction 19:19 Find eigenvalues with respect to x and to y 20:38 Calculate total eigenvalues of energy (E) Derivation of the wavefunction solutions for the 2-dimensional Particle in a Box problem, using the method of "separation of variables." See the wavefunctions illustrated here:    • Particle in a 2-D box wavefunctions illust...   Don't forget to like, comment, share, and subscribe!