How Do You Normalize a Quantum State in a Harmonic Oscillator?

[EEnerd]

Homework Statement

consider a harmonic oscillator of mass m and angular frequency ω, at time t=0 the state if this oscillator is given by
|ψ(0)>=c1|Y0> + c2|Y1> where |Y1> , |Y2> states are the ground state and the first state respectively

find the normalization condition for |ψ(0)> and the mean value for the energies <H> in terms of C0 and C1, (b)and if we assume <H>= hω calculate c0 and c1

Homework Equations

The Attempt at a Solution

ok i know that |c0|^2 +|c1|^2 =1

and <ψ|H|ψ>= E0|c0|^2 + E1|c1|^2 where E0=1/2 ωh and E1= 3/2 ωh

?!

 

[Dick]

Homework Statement

consider a harmonic oscillator of mass m and angular frequency ω, at time t=0 the state if this oscillator is given by
|ψ(0)>=c1|Y0> + c2|Y1> where |Y1> , |Y2> states are the ground state and the first state respectively

find the normalization condition for |ψ(0)> and the mean value for the energies <H> in terms of C0 and C1, (b)and if we assume <H>= hω calculate c0 and c1

Homework Equations

The Attempt at a Solution

ok i know that |c0|^2 +|c1|^2 =1

and <ψ|H|ψ>= E0|c0|^2 + E1|c1|^2 where E0=1/2 ωh and E1= 3/2 ωh

?!

Well, keep going. You've got two equations in the two unknowns |c0|^2 and |c1|^2. You won't be able to determine c0 and c1 but you can find their absolute values.