Hard Core Produced by Orthogonality Constraints

It is shown that the effect of a hard core as an external force can be reproduced by requirements of orthogonality alone. A fictitious orthonormal set of functions is introduced, which form a complete set in the domain occupied by the hard core. The actual wave function is constructed as the eigenfunction of a modified kinetic energy operator, and is required to be orthogonal to all members of the fictitious set. The limit of infinitely many constraints is carefully discussed. It turns out to be impossible to regard the hard core effect as equivalent to some kind of ``potential'' acting on free waves (for which the Hamiltonian would be well defined). However, the eigenfunction is well defined in the limit of infinitely many constraints, and is independent of the way in which the fictitious set is chosen.