How Does Changing Box Size Affect a Particle's Quantum State?

[TPDC130]

Hi, I am new to these concepts and i need help on answering some assignment questions.

the question is:
a particle of mass m is confined in a 1-d box of width L in the third excited state.
a) suppose the width of the box is suddenly doubled. find the probability that the particle remains in the same state.
b) calculate the prob that the particle drops to ground state when size is doubled.
c) calculate the probability that the particle initially in ground state remains in round state when size of box is reduced to L/2

i have no idea where to start on this and any help would be great

 

[malawi_glenn]

This will be moved to the Home Work section.

Please show you attempt to solution, if you don't have any idea, make atl east a serious guess.

Also write down the equations and formulas that you are familiar with. (eg. what a square well is, etc)

Since you are new here, I am nice to you and will give you a hint, in the future - read and follow the rules.

Hint: start by solving the Shrodinger equation for a square well with length $\nu L$, where $\nu = 1,2,3, ...$

 

[TPDC130]

ok, I am sorry for not including much. i didnt realize. this is new to me as i said. anyway, i am able to solve and get the wavefunction which turns out to be psi(x)=Asin(kx). and if i did my calculations correct, i think the energy in the 3rd excited state is given by E=(16*pi^2*hbar^2)/(2*m*L). i know how to find the probability that's its in a certain part of the box i.e. between L/2 and 3L/4 for example. but i have no idea to find the probability that its in a certain state or the prob that its still in that state when the well size is increased

 

[reilly]

You have two sets of eigenstates, one for L and one for 2L. Can you expand one set of eigenstates in terms of the other? If so, why would you want to do so?
Good luck
Reilly Atkinson