QM based on p93 1. wavefuction (represents state) .... vectors 2.operators (represents observables).... linear transformations linear algebra in N dimension a vector 3.1 inner product 3.2 linear transformations T (specified basis) 3.3 vector (functions) the integral must converge 3.4 wave functions live in hilbert space inner product of two functions 3.6 if f, g are square integrable in hilbert space 保證收斂 by 3.7 3.8 3.9 normalize inner product 1 orthogonal inner product 0 orthonormal inner product 3.10 a function is complete if any functions( in hilbert space) can be expressed as linear combination 3.11 if functions are orthonormal coifficients (by fourier tricks) 3.12 p96 {3.2} observables hermitian operators expectation value of observables are next to inner product notation 3.13 real 3.14 conjugate(in inner product) reverse order 3.15 thus for wave functions 3.16 called such operators hermitian ( hermitian 可作用在前或著後) 3.17 by pr 3.3 observables are represents by hermitian operators