When this quantity is well-defined, it must be conserved, a requirement that implies that the Hamiltonian must be Hermitian.
A factor of the square root of the density of states translates from discrete to continuous eigenfunctions, and from discrete to continuous amplitudes of this quantity, when the box normalization is employed for an operator whose eigenvalue spectrum includes a set of discrete values and a continuous range of values. The continuity equation for this quantity contains a term equal to the divergence of the real part of the conjugate of the wavefunction times minus i h-bar over m times the gradient of the wavefunction; (*) the expression acted on by the divergence defines this quantity's current density. When this quantity is well-defined, it must be conserved, a requirement that implies that the Hamiltonian must be Hermitian. This quantity is not well-defined for systems described by plane waves and other non-square-integrable wavefunctions. For 10 points, the square of the wavefunction was interpreted by Max Born as the density of what quantity, the likelihood of a given state?
A factor of the square root of the density of states translates from discrete to continuous eigenfunctions, and from discrete to continuous amplitudes of this quantity, when the box normalization is employed for an operator whose eigenvalue spectrum includes a set of discrete values and a continuous range of values.
probability density 