A series of videos explaining quantum mechanics, using math but with more emphasis on intuition than you will find in most textbooks. If you think you’re an idiot when it comes to learning these tough subjects, you might benefit by learning from me, a fellow idiot.
Topics covered in the Differential Equations playlist are orthogonal polynomials, Legendre and associated Legendre functions, Spherical harmonics, Bessel and Spherical functions, Laguerre and associated Laguerre polynomials, Hermite polynomials, and the Frobenius method. The videos that come after this point all assume you understand these concepts.
Topics covered are eigenvectors, eigenvalues, and their relationship to Hermitian operators
Topics covered are bases, components, inner product, and outer product using Dirac notation
Topics covered are Hermitian matrices and their properties, including the matrix transpose, complex conjugation of matrices, the determinant, and the trace or a matrix
A brief introduction to Paul Dirac’s Bra Ket notation
I talk about the nature of Hilbert space, which is essentially a complete, normed, inner product space. What does any of that mean? Watch the video to find out.
Topics discussed are the dual basis and their covariant and contravariant components
Rotation matrices and how each matrix element effects a vector
