Yes, eigenfunctions of self-adjoint operators are always orthogonal. See Spectral theorem for more details. Under some very general conditions on the potential, the eigenfunctions are always orthogonal. See also Sturm–Liouville theory.

For the discussion of why there are transitions between eigenstates, see Why do excited states decay if they are eigenstates of Hamiltonian and should not change in time?.

Yes, eigenfunctions of self-adjoint operators are always orthogonal. See Spectral theorem for more details. Under some very general conditions on the potential, the eigenfunctions are always orthogonal. See also Sturm–Liouville theory.

For the discussion of why there are transitions between eigenstates, see Why do excited states decay if they are eigenstates of Hamiltonian and should not change in time?.

Yes, eigenfunctions of self-adjoint are always orthogonal. See Spectral theorem for more details.

For the discussion of why there are transitions between eigenstates, see Why do excited states decay if they are eigenstates of Hamiltonian and should not change in time?.

Yes, eigenfunctions of self-adjoint operators are always orthogonal. See Spectral theorem for more details. Under some very general conditions on the potential, the eigenfunctions are always orthogonal. See also Sturm–Liouville theory.

For the discussion of why there are transitions between eigenstates, see Why do excited states decay if they are eigenstates of Hamiltonian and should not change in time?.