- #1
Lebnm
- 31
- 1
I have two question about a exemple given in the Sakurai's quantum mechanics book, section 4.3. Let's consider an electron in a periodic potential ##V(x + a) = V(x)##, that has the form of a wave. We will take the potential to go to infinity between two latteces sites, such that its form change to something like this : ...U U U U U U ... In this case, the book says that one possible candidate to the ground state of the system is a state ##|n \rangle## where the electron is completely localized in the ##n##th site, and so we have ##\hat{H}|n\rangle = E_{0} |n \rangle##. But why? I can't see why this state have to be the lowest energy state.
The second question is: Let's go back to the first case, where the potential is finite. In this case, the states ##|n \rangle## are not more hamiltonian eigenstates, that is, ##H## is not diagonal in this basis. I also don't understend why this happen. This seems intuitive, but I can't find a good reason for this.
The second question is: Let's go back to the first case, where the potential is finite. In this case, the states ##|n \rangle## are not more hamiltonian eigenstates, that is, ##H## is not diagonal in this basis. I also don't understend why this happen. This seems intuitive, but I can't find a good reason for this.