# Wave function of a simple harmonic oscillator

1. Oct 5, 2009

### noblegas

1. The problem statement, all variables and given/known data
The ground state wave function of a one-dimensional simple harmonic oscillator is

$$\varphi_0(x) \propto e^(-x^2/x_0^2)$$, where $$x_0$$ is a constant. Given that the wave function of this system at a fixed instant of time is $$\phi\phi \propto e^(-x^2/y^2)$$ where y is another constant., find the probablity, that if the energy is measured , the system will be in the ground state

2. Relevant equations

3. The attempt at a solution

$$dP=|\varphi_0|^2 dx$$

According to my book(Peebles) , $$=|\varphi_0|^2=|\phi_0|^2$$;, so therefore $$dP=|\phi_0|^2 dx$$?

2. Oct 5, 2009

### noblegas

anyone still not understand my question?

3. Oct 6, 2009

### sleventh

hello noble,
i'm wondering if you take the integral of your state function from 0 to infinity then divide that result the integral of your ground state function from 0-infinity will you get a function dependent on energy, whereas you could use an energy sample at any time to give the probability?