When a quantum system with continuous spectrum has a definite anergy, ordinary quantum mechanics uses a single continuous stationary state to describe its properties, the expectation values for arbitrary physical quantities are therefore either infinity or zero. In this paper we point out in the form of mathematical theorem that the system possesses new and deterministic results with evident physical meanings. Classical results for the system are the classical limit cases of these results, and the ordinarv expectation values are the statistical cases of our results.