# Superposition of states and orthonormalization

• tarletontexan

## Homework Statement

Consider a particle in a superposition of states given at time t=0 by Y(x,0)=C(y1(x)+y2(x)), where y1(x) and y2(x) are the stationary states with energies E1 and E2 respectively. if y1(x) and y2(x) are orthonormalized, what value of C is required to normalize Y(x,0)?

## The Attempt at a Solution

the orthonormalization is messing with my head, there is an example of normalizing wavefunctions in my book but this looks nothing like it. I am not sure of how to approach this problem.

What equation expresses the requirement that Y(x,0) is normalized?

that is not given, the only thing it asks for in this part of the problem is what value of C is required to normalize Y(x,0)...

I realize it is not given in the problem statement. It should be given in your lecture notes or textbook. What does it mean, for a wavefunction to be normalized? Use the definition of "normalized", and apply it to this problem.

ok, i see, but the example in the book has the initial wavefunction given as Y(x,0)=Cexp(-|x|/x0) where C and x0 are constants, is it possible to get this function into a similar format??