What happens to psi in Infinite potential well

[bs vasanth]

What happens to ψ in a infinite potential well when the width is suddenly reduced to half its previous value ?
Will this instantly adjust ψ to the new size of the well or will it take some time to confine itself in this new well ? And is there a possibility of quantum tunneling here?

 

[Matterwave]

It depends on the speed at which the walls move in. "Instantly" is probably not a good measure. If the move to the new size is slow, then by the adiabatic theorem, the wave function, assuming it was initially in an eigenstate of the Hamiltonian, will adjust to remain an eigenstate of the Hamiltonian. If the transition is fast, then the state is not guaranteed to do this, and in general, will end up as a superposition of energy eigenstates. How it transforms then depends on the details of how the "walls" move. There's no quantum tunneling when the potential is an infinite well. Where would the particle tunnel to?

 

[rigetFrog]

To expand on the above, the well with reduction may actually impart energy onto the electron driving it to higher energies. Kind of like squeezing a pimple till it pops. Except it won't pop unless the walls are finite.