A one-dimensional harmonic oscillator is in the ground state. At t=0, the spring is cut. Find the wave-function with respect to space and time (ψ(x,t)).
Note: At t=0 the spring constant (k) is reduced to zero.
So, my question is mostly conceptual. Since the spring constant goes to zero at t=0 is it safe to assume that the problem can now be considered as a free particle problem since the potential goes to zero when 'k' goes to zero?
If this assumption is correct I should be able to solve the time independent Schrodinger equation, ψ(x,0), then multiply in the time part and solve for the constant.
I do not see how being a harmonic oscillator will affect my answer since once you cut the spring it is no longer a harmonic oscillator.
Is there something I am missing conceptually?