1. The problem statement, all variables and given/known data Consider a 1-dimensional linear harmonic oscilator. Any measurement of it's energy can either return the value of ħw/2 or 3ħw/2, with equal probability. The mean value of the momentum <P> at the instant t=0 is <P> = (mħw/2)1/2 Find the wave function ψ(x,0) for this state. 2. Relevant equations 3. The attempt at a solution I started by assuming that the wave function would be something of the kind: ψ(x,0) = α|ϕ0> + β|ϕ1> Since the probability of measuring the energy for n=0 and n=1 is the same I concluded that α=β Image with my resolution: http://oi41.tinypic.com/2e64ykz.jpg I think my way of solving the problem is correct, however the result doesn't make sense... If someone could give me a hint about where I might have gone wrong I'd appreciate. Thanks.