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)?

Homework Equations

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.

 

[Redbelly98]

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

 

[tarletontexan]

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)...

 

[Redbelly98]

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.

 

[tarletontexan]

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??