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## Homework Statement

Hi all. My question is best illustrated with an example. Please, take a look:

Let's say we have particle in a stationary state, so [tex]\Psi(x,0)=1\cdot \psi_{1,0}(x)[/tex] with energy

*E_{1,0}*. Now at time

*t=0*the Hamiltonian of this particle changes, since the particle gains some energy. Thus the wavefunction [tex]\Psi(x,t)[/tex] changes, and it can be written as:

[tex]

\Psi(x,t)=\sum_{n=1}^\infty{c_n\psi_{2,n}e^{-iE_nt/\hbar}},

[/tex]

where [tex]\psi_{2,n}(x)[/tex] are the new stationary states.

**Question:**At time

*t=0*when the particle gains energy and hence [tex]\Psi(x,t)[/tex] changes, is the wavefunction given as:

[tex]

\Psi (x,0) = \psi _{1,0} (x) = \sum\limits_{n = 0}^\infty {c_n } \psi _{2,n} (x)

[/tex]

So does the wavefunction change immediately or does it evovle in a slow fashion?