Approximations for the Lowest Energy Eigenstates in a Double Square Well Potential

Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between (so that the potential is a sequence of five constant pieces that alternate in value from being above and below the ground state and first excited state energies), under the assumption that the barrier is sufficiently wide that the tunneling across it is very small.