Quantum mechanics tells us that any quantum particle behaves as particle or waves in different situations. Assume that the electron is behaving like wave in some situation, how can I visualise this situation. Whether the electron is continuously vibrating about its position or not? In internet I read that a single electron in hydrogen atom mostly behaves as wave . In that it is compared to the stranding waves on the guitar string I just want to know what it is doing when it is behaving as wave and as particle Please clarify this,otherwise I simply waste my time by keep on searching in Google ..... Please...
It is a bit like the standing wave, but the "particle" (electron, in your example) would correspond to an excitation of the string, not the string itself. The string itself would represent the "wave function" of the electron.
But it's a string with a very strange property: it is either vibrating with a particular amplitude, or it is not vibrating at all. Vibrating means that the electron exists, not vibrating means it does not exist. This strange property is how the Pauli exclusion principle would work in your model: only one excitation allowed <=> only one electron per quantum state.
Believe me, it takes a while to get used to thinking about things this way. There really is no adequate analog or metaphor in our everyday experience that can be used to develop the visualization that you seek. In particular: don't think about a vibrating particle. That picture is far enough removed from real electron behavior that it is fruitless.