Quantum Mechanics Made Easy

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.

Listed here in reverse order (newest to oldest)

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This would be a good point to check out my Youtube playlist on the special functions of differential equations if you are unfamiliar with the subject.

differential equations special functions orthogonal polynomials

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
Vector operations, including matrix transformation, dot product (aka scalar product aka inner product), cross product (aka vector product), triple scalar product, and triple vector product
How coordinates transform in linear algebra
Introduction to the concept of vectors