Normalizing psi in harmonic oscillator

[3uc1id]

My question is pretty easy (i think). I have a wavefcn PSI defined at t=0. The PSI is a mix of several eigenstates. Let's say PHI(x,0)=C1phi1 + C2 phi3. Now C1 and C2 are given to me, so I am wondering is this wavefcn. already normalized, or do i have to normalize it despite definite C1 and C2 already being given?

 

[Cyosis]

Since phi1 and phi2 are eigenstates they should be normalized already. I suggest you take the integral with C1 and C2 plugged in and see if it yields one. In other words show that $|C_1|^2+|C_2|^2=1$.

 

[3uc1id]

thank you.