A particle is initially in the ground state of the harmonic oscillator with classical frequency ω. Suddenly, the spring constant increases, causing the frequency to change to \(ω' = 2ω\), but the wave function remains unchanged initially (although it will evolve differently after the change due to the modified Hamiltonian). What is the probability that a measurement of the energy would still yield the value ħω/2? What is the probability of measuring ħω'?
1
\(P_0 = 1.0000\)
2
\(P_0 = 0.9428\)
3
\(P_0 = 0.0572 \)
4
None of the above