1. The problem statement, all variables and given/known data particle in ground state of 1D harmonic oscillator - spring constant is doubled - what is the probability of finding the particle in the ground state of the new potential 2. Relevant equations v=1/2kx^2 oscillator potential wavefunction ground state n=0 = (alpha/pi)^1/4*e^[(-apha*x^2)/2] alpha = sqroot[(k*m)/hbar^2)] 3. The attempt at a solution the probability will be = integral[wavefunction old*wavefunction new]dx initial equation d^2psi/dx^2 + [2m(E-1/2kx^2)/hbar]psi = 0 if you double k in the potential V(x)- the equation is d^2psi/dx^2 + [2m(E-kx^2)/hbar]psi = 0 does this change alpha to 2k? this makes the integral very complex to solve. or can this be done by changing the wavefunction for the new potential to (alpha/2pi)^1/4*e^[(-apha*x^2)/2] the change being 2pi - doubling the range of the spring constant? Thanks!