394 Quantum mechanics
9.10 A single particle in one dimension is subject to a potentialU(x). Another
particle in one dimension is subject to a potentialV(x). SupposeU(x) 6 =
V(x) +C, whereCis a constant. Prove that the ground-state wave functions
ψ 0 (x) andφ 0 (x) for each problem must be different.Hint: Try using proof by contradiction. That is, assumeψ 0 (x) =φ 0 (x). What
relation betweenU(x) andV(x) is obtained?