Commuting of Operators: Particle in Box in 1D with H & H1

[hokhani]

consider a particle in the box in one dimension with the length a. the hamiltonian is H.
then the box's walls goes far away and the box length gets b. now the hamiltonian is H1.
i like to know whether these two hamiltonians commute or not?

 

[bp_psy]

What is the difference between your H and H1?

 

[hokhani]

for the first one dimensional box, two walls are located in the distance "a" while in another box they are in the distance "b"
so the boundary is different for them.
i want to now if H and H1 have the same eigenvectors!?

 

[bp_psy]

Write down the Hamiltonians and solve the Equation with the boundaries and you will see.

 

[hokhani]

ok
thanks
i find my misunderestanding
i thought both have the same hamiltonian "p^2/2m" so they should have the same eigenvectors.