EQUISPACED-LEVEL HAMILTONIANS WITH THE VARIABLE EFFECTIVE-MASS FOLLOWING THE POTENTIAL

A coordinate-transform-based procedure is presented for generating Ham iltonians with the effective-mass variation proportional to the potent ial variation, and having equispaced bound states. A situation like th at occurs in graded semiconductor quantum wells based on ternary alloy s, e.g., AlxGa1-xAs, and the procedure aims at designing the structure to have equispaced states. Two types of Hamiltonians are derived, one with the confining potential that may be realized by appropriate grad ing of the alloy, and another with a nonconforming potential but with the effective mass tending to zero at infinity. This latter type of Ha miltonian is not realizable in semiconductor structures, but gives ins ight into the nature of wave-function confinement, which makes it inte resting in its own right.