A realistic interpretation(REIN) of wave function in quantum mechanics is briefly presented in this work. In REIN, the wave function of a microscopic object is just its real existence rather than a mere mathematical description. Quantum object can exist in disjoint regions of space which just as the wave function distributes, travels at a finite speed, and collapses instantly upon a measurement. The single photon interference in a MachZehnder interferometer is analyzed using REIN. In particular, we proposed and experimentally implemented a generalized delayed-choice experiment, the encounter-delayed-choice(EDC) experiment, in which the second beam splitter is inserted at the encounter of the two sub-waves from the two arms. In the EDC experiment, the front parts of wave functions before the beam splitter insertion do not interfere and show the particle nature, and the back parts of the wave functions will interfere and show a wave nature. The predicted phenomenon is clearly demonstrated in the experiment, and supports the REIN idea.PACS numbers: 03.65.Ta, 03.65.Ud, 42.50.Xa,42.50.DvThe wave-particle duality is a central concept of quantum mechanics and is strikingly illustrated in the well-known Wheeler's delayed-choice gedanken experiment [1][2][3][4][5][6][7][8][9]. A good demonstration of the delayed-choice experiment is given by a two-path interferometer, Mach-Zehnder interferometer (MZI), seen in Figure 1(a). A single photon is directed to the MZI followed by two detectors at its end. If the output beam splitter BS 2 is present (closed configuration), the photon is first split by the input beam splitter BS 1 and then travels inside the MZI with a tunable phase shifter φ until the two interfering paths are recombined by BS 2 . When φ is varied, the interference fringes are observed as a modulation of the detection probabilities of detectors D 1 and D 2 . It indicates that the photon travels both paths of the MZI to behave as a wave and the two paths are indistinguishable. If BS 2 is absent (open configuration), a click in only one of the two detectors with probability 1/2, independent of φ, is associated with a given path to indicate that the photon travels along a single path and behaves as a particle. Such an experiment concludes that quantum systems exhibit wave or particle behavior depending on the configuration of the measurement apparatus. Moreover, the two complementary experimental setups are mutually exclusive and the two behaviors, wave and particle behavior, cannot be observed simultaneously.Recently, a new extension of the delayed-choice experiment (quantum delayed-choice) [10][11][12][13][14][15][16][17], where the output beam splitter in this classical state is replaced with that in a quantum superposition state, has been proposed. The experiment indicates that BS 2 can be simultaneously absent and present, and both wave and particle behavior can be simultaneously observed to show a morphing behavior between wave and particle.The concept of a wave function is introduced to quantum theory as a c...