# I Transition probability and superposition

1. Apr 7, 2016

Hello
suppose that we are dealing with a particle moving in an infinite potential well(a box of length L).
Let the wavefunction of the particle be $\psi(x,t)=c1\psi_{1}(x,t)+....+cn\psi_{n}(x,t)$
suppose that after measurement we find the particle at the energy eigenstate $\psi_{1}(x,t)$.
Now lets change the size of the box to 2L. Lets find the probability of the particle being in state $\phi_{1}(x)$ which is the ground state of the new box.The answer is $|\int\phi^{*}_{1}(x)\psi_{1}(x)dx|^{2}$,which may in many cases be not equal to zero.
My confusion is here: what if we didn't change the box and we computed the same integral above, which is the probability of the particle to be in state $\phi_{1}(x)$ and it is a non allowed state, the probability of course will not be zero because it is the same integral above.
How the probability of the particle in being in a non allowed state can be not equal to zero ?

2. Apr 7, 2016

### Jilang

It's not the same integral as the limits are different.

3. Apr 7, 2016

No it is the same since $\psi_{1}(x)$=0 for x outside the interval [0,L].