Variational theorem proof: general case скачать в хорошем качестве

Variational theorem proof: general case

00:07 Variational theorem in symbols 00:17 Schrodinger equation 00:44 Ordering of eigenvalues 01:17 Trial solution function as summation of eigenfunctions 01:58 Expectation (average) value as summation of weighted eigenvalues 02:28 First inequality 02:34 Multiply each side of first inequality by non-negative constant 02:48 Second inequality (from ordering of eigenvalues) 02:57 Multiply each side of second inequality by non-negative constant 03:07 n-th inequality (from ordering of eigenvalues) 03:19 Multiply each side of n-th inequality by non-negative constant 03:34 Sum of each side of all inequalities 04:17 Left side of inequality equals smallest eigenvalue ("true" value) 04:21 Right side of inequality equals expectation value Proof of the Variational Theorem in the general case of a linear combination (superposition) of an infinite number of eigenfunctions.. Don't forget to like, comment, share, and subscribe!