Hi, material on learning the calculus way are plentiful but I can't find anywhere to teach me the matrix way, any links? I can't even find out how to represent the Hamiltonian as a matrix. Thanks in advance
Take a look also at the third volume of the Feynman lectures.
In a given basis, a vector has a representation as a column vector vi, where i is a discrete index. The number of indices is the dimension of the vector space. You can think of the position space wavefunction ψ(x) similarly as the representation of a vector in the position basis, except that the index x is continuous. Since there are now an infinite number of indices, the dimension of the vector space is infinite. There are differences between finite and infinite dimensional vector spaces, but using the finite dimensional case for intuition is roughly ok. Now sticking to the finite dimensional case, if we think of the state as a column vector in a certain basis, an operator on the state can be represented as a matrix.