As a 1-dimensional problem, you have Schrodinger's equation, given by: a -h? a2 iħ (x, t) =- at 2m Əx? 4(x, t) + V(x) Þ(x,t) Suppose for a specific V(x) and certain boundary conditions, the function w,(x, t) is a solution to the above equation and w2 (x, t) is also a solution. Show that 4(x, t) = a,(x, t) + b2(x, t) also solves the above equation, where a, b are complex numbers.

As a 1-dimensional problem, you have Schrodinger's equation, given by: a -h? a2 iħ (x, t) =- at 2m Əx? 4(x, t) + V(x) Þ(x,t) Suppose for a specific V(x) and certain boundary conditions, the function w,(x, t) is a solution to the above equation and w2 (x, t) is also a solution. Show that 4(x, t) = a,(x, t) + b2(x, t) also solves the above equation, where a, b are complex numbers.