Q1) Given the infinite square well V(x) = 0 for 0

A particle of mass m in the well has initial wave function like that of a triangle wave:

(x,0)= Ax for 0

(x,0)= A(2-x) for 1

(x,0)= 0 for elsewhere

1. Find the constant A
2. Find the wave function for this particle at subsequent times (x,t) by expressing as a linear combination of eigen states in the infinite square well
3. Find the expression of the summation coefficients (c_n) as a function of n. (i.e., solve the integral).