Quantum Mechanics for Engineers 

© Leon van Dommelen 

N.11 Better description of twostate systems
An approximate definition of the states and would
make the states and only approximate
energy eigenstates. But they can be made exact energy eigenfunctions
by defining and to
be the exact symmetric ground state and the exact antisymmetric state
of second lowest energy. The precise basic
wave
function and can then be reconstructed from that.
Note that and themselves are not energy eigenstates,
though they might be so by approximation. The errors in this
approximation, even if small, will produce the wrong result for the
time evolution. (The small differences in energy drive the
nontrivial part of the unsteady evolution.)